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BEGIN:VEVENT
SUMMARY:Jaehoon Lee (Seoul National University)
DTSTART;VALUE=DATE-TIME:20200925T093000Z
DTEND;VALUE=DATE-TIME:20200925T103000Z
DTSTAMP;VALUE=DATE-TIME:20230921T160806Z
UID:SeminarioGeometry/1
DESCRIPTION:Title: Closed Lagrangian Self-Shrinkers in $\\mathbb{R}^4$ Symmetric wi
th Respect to a Hyperplane\nby Jaehoon Lee (Seoul National University)
as part of Geometry Seminar\, Universidad de Granada (Spain)\n\nAbstract:
TBA\n
LOCATION:https://researchseminars.org/talk/SeminarioGeometry/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jorge de Lira (Universidad de Ceará)
DTSTART;VALUE=DATE-TIME:20201016T110000Z
DTEND;VALUE=DATE-TIME:20201016T120000Z
DTSTAMP;VALUE=DATE-TIME:20230921T160806Z
UID:SeminarioGeometry/2
DESCRIPTION:Title: Einstein type elliptic systems.\nby Jorge de Lira (Universid
ad de Ceará) as part of Geometry Seminar\, Universidad de Granada (Spain)
\n\n\nAbstract\nWe will discuss a type of semi-linear systems of partial d
ifferential equations which are motivated by the conformal formulation of
the Einstein constraint equations coupled with realistic physical fields o
n asymptotically flat manifolds. In particular\, electromagnetic fields gi
ve rise to this kind of systems. In this context\, under suitable conditio
ns\, we prove a general existence theorem for such systems\, and\, in part
icular\, under smallness assumptions on the free parameters of the problem
\, we prove existence of far from CMC (near CMC) Yamabe positive (Yamabe n
on-positive) solutions for charged dust coupled to the Einstein equations\
, satisfying a trapped surface condition on the boundary. As a bypass\, we
prove a Helmholtz decomposition on asymptotically flat manifolds with bou
ndary\, which extends and clarifies previously known results.\n
LOCATION:https://researchseminars.org/talk/SeminarioGeometry/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eddygledson Souza Gama (Universidade Federal Rural do Semi-Árido
(Brasil))
DTSTART;VALUE=DATE-TIME:20201030T120000Z
DTEND;VALUE=DATE-TIME:20201030T130000Z
DTSTAMP;VALUE=DATE-TIME:20230921T160806Z
UID:SeminarioGeometry/3
DESCRIPTION:Title: A barrier principle at infinity for varifolds with bounded mean
curvature\nby Eddygledson Souza Gama (Universidade Federal Rural do Se
mi-Árido (Brasil)) as part of Geometry Seminar\, Universidad de Granada (
Spain)\n\n\nAbstract\nIn this lecture\, we are going to talk about a versi
on of the barrier principle for varifolds at infinity. The main aims of th
is lecture is to prove the validity of the equality\n\n$\\mathrm{dist}(\\p
artial\\Omega\,\\mathrm{spt}\\|\\Sigma\\| )= \\mathrm{dist}(\\partial\\Ome
ga\,\\mathrm{spt}\\|\\partial\\Sigma\\| )\, $\n\nwhen $\\Omega$ is an open
set in a complete Riemannian manifold \\(M\\) both with a particular stru
cture and $\\Sigma$ is varifolds with bounded mean curvature satisfies a p
articular condition. This work was done jointly with Jorge H. de Lira (Uni
versidad Federal do Ceará)\, Luciano Mari (Universitá degli Studi di T
orino) and Adriano A. de Medeiros (Universidade Federal da Paraı́ba)\n\n
222601\n
LOCATION:https://researchseminars.org/talk/SeminarioGeometry/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alberto Roncoroni (University of Granada)
DTSTART;VALUE=DATE-TIME:20201106T103000Z
DTEND;VALUE=DATE-TIME:20201106T113000Z
DTSTAMP;VALUE=DATE-TIME:20230921T160806Z
UID:SeminarioGeometry/4
DESCRIPTION:Title: Classification of solutions to the critical p-Laplace equations<
/a>\nby Alberto Roncoroni (University of Granada) as part of Geometry Semi
nar\, Universidad de Granada (Spain)\n\n\nAbstract\nWe consider the follow
ing critical $p$-Laplace equation: \n\n$(1)\\qquad \\Delta_p u+u^{p^{\\ast
}-1}=0 \\quad \\text{ in $\\mathbb{R}^n$}\, $\n\nwith $n \\geq 2$ and $1 <
p < n$. Equation \\eqref{p-Laplace} has been largely studied in the PDE's
and geometric analysis' communities\, since extremals of Sobolev inequali
ty solve \\eqref{p-Laplace} and\, for $p=2$\, the equation is related to t
he Yamabe's problem. In particular\, it has been recently shown\, exploiti
ng the moving planes method\, that positive solutions to (1) such that \n$
u\\in L^{p^\\ast}(\\mathbb{R}^n)$ and $\\nabla u\\in L^p(\\mathbb{R}^n)$ c
an be completely classified. In the talk we will consider the anisotropic
critical $p$-Laplace equation in convex cones of $\\mathbb{R}^n$. Since th
e moving plane method strongly relies on the symmetries of the equation an
d of the domain\, in the talk a different approach to this problem will be
presented. In particular this approach gives a complete classification of
the solutions in an anisotropic setting. More precisely\, we characterize
solutions to the critical $p$-Laplace equation induced by a smooth norm i
nside any convex cone of $\\mathbb{R}^n$.\n%which allows us to give a comp
lete classification of the solutions in an anisotropic setting as well as
to a suitable generalization of the problem in convex cones\n\nThis is a j
oint work with G. Ciraolo and A. Figalli.\n
LOCATION:https://researchseminars.org/talk/SeminarioGeometry/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:José Miguel Manzano (University of Jaén)
DTSTART;VALUE=DATE-TIME:20201120T093000Z
DTEND;VALUE=DATE-TIME:20201120T103000Z
DTSTAMP;VALUE=DATE-TIME:20230921T160806Z
UID:SeminarioGeometry/5
DESCRIPTION:Title: Horizontal Delaunay surfaces with constant mean curvature in pro
duct spaces\nby José Miguel Manzano (University of Jaén) as part of
Geometry Seminar\, Universidad de Granada (Spain)\n\n\nAbstract\nIn this t
alk\, we will describe the 1-parameter family of horizontal Delaunay surfa
ces in $\\mathbb{S}^2\\times\\mathbb{R}$ and $\\mathbb{H}^2\\times\\mathbb
{R}$ with supercritical constant mean curvature. These surfaces are not eq
uivariant but singly periodic\, and they lie at bounded distance from a ho
rizontal geodesic. We will show that horizontal unduloids are properly emb
edded surfaces in $\\mathbb{H}^2\\times\\mathbb{R}$. We also describe the
first non-trivial examples of embedded constant mean curvature tori in $\\
mathbb{S}^2\\times\\mathbb{R}$ which are continuous deformations from a st
ack of tangent spheres to a horizontal invariant cylinder. They have const
ant mean curvature $H>1/2$. Finally\, we prove that there are no properly
immersed surface with critical or subcritical constant mean curvature at b
ounded distance from a horizontal geodesic in $\\mathbb{H}^2\\times\\mathb
b{R}$.\n
LOCATION:https://researchseminars.org/talk/SeminarioGeometry/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:João Paulo dos Santos (Universidade do Brasília)
DTSTART;VALUE=DATE-TIME:20201218T120000Z
DTEND;VALUE=DATE-TIME:20201218T133000Z
DTSTAMP;VALUE=DATE-TIME:20230921T160806Z
UID:SeminarioGeometry/6
DESCRIPTION:Title: Hypersurfaces of constant higher order mean curvature in $M×\\m
athbb{R}$\nby João Paulo dos Santos (Universidade do Brasília) as pa
rt of Geometry Seminar\, Universidad de Granada (Spain)\n\n\nAbstract\nWe
consider hypersurfaces of products $M\\times \\mathbb{R}$ with constant r-
th mean curvature — to be called $H_r$-hypersurfaces — where $M$ is an
arbitrary Riemannian manifold. We develop a general method for constructi
ng them\, and employ it to produce many examples for a variety of manifold
s $M$\, including all simply connected space forms and the Hadamard manifo
lds known as Damek-Ricci spaces. Uniqueness results for complete $H_r$-hyp
ersurface of $\\mathbb{H}^n\\times\\mathbb{R}$ or $\\mathbb{S}^n\\times\\m
athbb{R}$ $(n \\geq 3)$ are also obtained. This is a joint work with Ronal
do de Lima (UFRN) and Fernando Manfio (ICMC-USP).\n
LOCATION:https://researchseminars.org/talk/SeminarioGeometry/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jesús Castro-Infantes (University of Granada)
DTSTART;VALUE=DATE-TIME:20210219T110000Z
DTEND;VALUE=DATE-TIME:20210219T120000Z
DTSTAMP;VALUE=DATE-TIME:20230921T160806Z
UID:SeminarioGeometry/7
DESCRIPTION:Title: A construction of constant mean curvature surfaces in $\\mathbb
{H}^2\\times \\mathbb{R}$ and the Krust property\nby Jesús Castro-Inf
antes (University of Granada) as part of Geometry Seminar\, Universidad de
Granada (Spain)\n\n\nAbstract\nIn this talk we will construct via Daniel
's sister correspondence in $\\mathbb H^2\\times\\mathbb R$ a 2-parameter
family of Alexandrov-embedded constant mean curvature $0\\\,$<$\\\,H\\leq
1/2$ surfaces in $\\mathbb H^2\\times \\mathbb R$ with $2$ ends and genus
$0$. They are symmetric with respect to a horizontal slice and $k$ vertic
al planes disposed symmetrically. We will discuss the embeddedness of the
constant mean curvature surfaces of this family\, and we will show that
the Krust property does not hold for $0\\\,$<$\\\,H\\leq1/2$\; i.e\, there
are minimal graphs over convex domain in $\\widetilde{\\text{SL}}_2(\\mat
hbb R)$ and $\\text {Nil}_3$ whose sister conjugate surface is not a verti
cal graph in $\\mathbb H^2\\times\\mathbb R$.\n
LOCATION:https://researchseminars.org/talk/SeminarioGeometry/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Franc Forstnerič (University of Ljubljana)
DTSTART;VALUE=DATE-TIME:20210312T110000Z
DTEND;VALUE=DATE-TIME:20210312T120000Z
DTSTAMP;VALUE=DATE-TIME:20230921T160806Z
UID:SeminarioGeometry/8
DESCRIPTION:Title: Schwarz-Pick lemma for harmonic maps which are conformal at a po
int\nby Franc Forstnerič (University of Ljubljana) as part of Geometr
y Seminar\, Universidad de Granada (Spain)\n\n\nAbstract\nWe obtain a shar
p estimate on the norm of the differential of a harmonic map from the unit
disc ${\\mathbb D}$ in $\\C$ to the unit ball ${\\mathbb B}^n$ in $\\R^n$
\, $n\\ge 2$\, at any point where the map is conformal. In dimension $n=2$
this generalizes the classical Schwarz-Pick lemma to harmonic maps $\\mat
hbb D\\to\\mathbb D$ which are conformal only at the reference point. In d
imensions $n\\ge 3$ it gives the optimal Schwarz-Pick lemma for conformal
minimal discs $\\mathbb D\\to {\\mathbb B}^n$. Let ${\\mathcal M}$ denote
the restriction of the Bergman metric on the complex $n$-ball to the real
$n$-ball ${\\mathbb B}^n$. We show that conformal harmonic immersions $M \
\to ({\\mathbb B}^n\,{\\mathcal M})$ from any hyperbolic open Riemann surf
ace $M$ with its natural Poincar\\'e metric are distance-decreasing\, and
the isometries are precisely the conformal embeddings of $\\mathbb D$ onto
affine discs in ${\\mathbb B}^n$. (Joint work with David Kalaj.)\n
LOCATION:https://researchseminars.org/talk/SeminarioGeometry/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ezequiel Barbosa (Universidad de Granada)
DTSTART;VALUE=DATE-TIME:20210305T110000Z
DTEND;VALUE=DATE-TIME:20210305T120000Z
DTSTAMP;VALUE=DATE-TIME:20230921T160806Z
UID:SeminarioGeometry/9
DESCRIPTION:Title: On non-compact free boundary minimal hypersurfaces in the Rieman
nian Schwarzschild spaces\nby Ezequiel Barbosa (Universidad de Granada
) as part of Geometry Seminar\, Universidad de Granada (Spain)\n\n\nAbstra
ct\nWe will show that\, in contrast with the 3-dimensional case\, the Mors
e index of a free boundary rotationally symmetric totally geodesic hypersu
rface of the $n$-dimensional Riemannnian Schwarzschild space with respect
to variations that are tangential along the horizon is zero\, for $n\\geq4
$. Moreover\, we will show that there exist non-compact free boundary mini
mal hypersurfaces which are not totally geodesic\, $n\\geq 8$\, with Morse
index equal to 0. Also\, for $n\\geq4$\, there exist infinitely many non-
compact free boundary minimal hypersurfaces\, which are not congruent to
each other\, with infinite Morse index. Finally\, we will discuss the dens
ity at infinity of a free boundary minimal hypersurface with respect to a
minimal cone constructed over a minimal hypersurface of the unit Euclidean
sphere. We obtain a lower bound for the density in terms of the area of t
he boundary of the hypersurface and the area of the minimal hypersurface i
n the unit sphere. This lower bound is optimal in the sense that only mini
mal cones achieve it.\n
LOCATION:https://researchseminars.org/talk/SeminarioGeometry/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marilena\, Moruz (Al.I. Cuza University of Iasi)
DTSTART;VALUE=DATE-TIME:20210409T100000Z
DTEND;VALUE=DATE-TIME:20210409T110000Z
DTSTAMP;VALUE=DATE-TIME:20230921T160806Z
UID:SeminarioGeometry/10
DESCRIPTION:Title: Ruled real hypersurfaces in $\\mathbb CP^n_p$\nby Marilena\
, Moruz (Al.I. Cuza University of Iasi) as part of Geometry Seminar\, Univ
ersidad de Granada (Spain)\n\n\nAbstract\nH. Anciaux and K. Panagiotidou [
1] initiated the study of non-degenerate real hypersurfaces in non-flat in
definite complex space forms in 2015. Next\, in 2019 M. Kimura and M. Orte
ga [2] further developed their ideas\, with a focus on Hopf real hypersurf
aces in the indefinite complex projective space $\\mathbb CP^n_p$. In this
work we are interested in the study of non-degenerate ruled real hypersur
faces in $\\mathbb CP^n_p$. We first define such hypersurfaces\, then give
basic characterizations. We also construct their parameterization. They a
re described as follows. Given a regular curve $\\alpha$ in $\\mathbb CP^n
_p$\, then the family of the complete\, connected\, complex $(n − 1)$-di
mensional totally geodesic submanifolds orthogonal to $\\alpha'$ and $J\\a
lpha'$\, where $J$ is the complex structure\, generates a ruled real hyper
surface. This representation agrees with the one given by M. Lohnherr and
H. Reckziegel in the Riemannian case [3]. Further insights are given into
the cases when the ruled real hypersurfaces are minimal or have constant s
ectional curvatures. The present results are part of a joint work together
with prof. M. Ortega and prof. J.D. Pérez. \n\n[1] H. Anciaux\, K. Panag
iotidou\, Hopf Hypersurfaces in pseudo-Riemannian complex and para-complex
space forms\, Diff. Geom. Appl. 42 (2015) 1-14.\n\n[2] M. Kimura\, M. Ort
ega\, Hopf Real Hypersurfaces in Indefinite Complex Projective\, Mediterr.
J. Math. (2019) 16:27.\n\n[3] M. Lohnherr\, H. Reckziegel\, On ruled real
hypersurfaces in complex space forms. Geom. Dedicata 74 (1999)\, no. 3\,
267–286.\n
LOCATION:https://researchseminars.org/talk/SeminarioGeometry/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brian White (Stanford University)
DTSTART;VALUE=DATE-TIME:20210325T160000Z
DTEND;VALUE=DATE-TIME:20210325T170000Z
DTSTAMP;VALUE=DATE-TIME:20230921T160806Z
UID:SeminarioGeometry/11
DESCRIPTION:Title: Mean Curvature Flow with Boundary\nby Brian White (Stanford
University) as part of Geometry Seminar\, Universidad de Granada (Spain)\
n\n\nAbstract\nAlmost all of the extensive research on mean curvature flow
has been for surfaces without boundary. However\, it is interesting and n
atural to consider MCF for surfaces with boundary. In this talk\, I will d
escribe a useful weak formulation of such flows that gives existence for a
ll time with arbitrary initial data. Furthermore\, under rather mild hypot
heses on the initial surface\, the moving surface remains forever smooth a
t the boundary\, even after singularities may have formed in the interior.
On the other hand\, if one relaxes those hypotheses\, then interesting bo
undary singularities can occur.\n
LOCATION:https://researchseminars.org/talk/SeminarioGeometry/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pozuelo\, Julián (University of Granada)
DTSTART;VALUE=DATE-TIME:20210416T100000Z
DTEND;VALUE=DATE-TIME:20210416T110000Z
DTSTAMP;VALUE=DATE-TIME:20230921T160806Z
UID:SeminarioGeometry/12
DESCRIPTION:Title: Existence of isoperimetric regions in sub-Finsler nilpotent gro
ups\nby Pozuelo\, Julián (University of Granada) as part of Geometry
Seminar\, Universidad de Granada (Spain)\n\n\nAbstract\nWe consider a nilp
otent Lie group with a bracket-generating distribution $\\mathcal{H}$ and
an asymmetric left-invariant norm $\\|\\cdot\\|_K$ induced by a convex bod
y $K\\subseteq\\mathcal{H}_0$ containing $0$ in its interior. In this talk
\, we will associate a left-invariant perimeter functional $P_K$ to $K$ fo
llowing De Giorgi's definition of perimeter and prove the existence of min
imizers of $P_K$ under a volume (Haar measure) constraint. We will also di
scuss some properties of the isoperimetric regions and the isoperimetric p
rofile.\n
LOCATION:https://researchseminars.org/talk/SeminarioGeometry/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Graham Smith (Universidade Federal do Rio de Janeiro)
DTSTART;VALUE=DATE-TIME:20210430T110000Z
DTEND;VALUE=DATE-TIME:20210430T120000Z
DTSTAMP;VALUE=DATE-TIME:20230921T160806Z
UID:SeminarioGeometry/13
DESCRIPTION:Title: The Kulkarni-Pinkall form and locally strictly convex immersion
s in $\\mathbb{H}^3$\nby Graham Smith (Universidade Federal do Rio de
Janeiro) as part of Geometry Seminar\, Universidad de Granada (Spain)\n\n\
nAbstract\nIn this talk we study applications of the Kulkarni-Pinkall form
to the study of locally strictly convex immersions in $\\mathbb{H}^3$. We
deduce a new a priori estimate which in turn allows us to completely solv
e the asymptotic Plateau problem for $k$-surfaces in hyperbolic space as f
ormulated by Labourie. This work has interesting intersections with a pape
r of Espinar-Galvez-Mira. This work appears in https://arxiv.org/abs/2104.
03181.\n
LOCATION:https://researchseminars.org/talk/SeminarioGeometry/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gianmarco Giovannardi (Universidad de Granada)
DTSTART;VALUE=DATE-TIME:20210528T100000Z
DTEND;VALUE=DATE-TIME:20210528T110000Z
DTSTAMP;VALUE=DATE-TIME:20230921T160806Z
UID:SeminarioGeometry/14
DESCRIPTION:Title: The Bernstein problem for Euclidean Lipschitz surfaces in the s
ub-Finsler Heisenberg group $\\mathbb{H}^1$\nby Gianmarco Giovannardi
(Universidad de Granada) as part of Geometry Seminar\, Universidad de Gran
ada (Spain)\n\n\nAbstract\nWe shall prove that in the first Heisenberg gro
up with a sub-Finsler structure\, a complete\, stable\, Euclidean Lipschit
z and $H$-regular surface is a vertical plane. This is joint work with Man
uel Ritoré.\n
LOCATION:https://researchseminars.org/talk/SeminarioGeometry/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Or Hershkovits (Hebrew University of Jerusalem)
DTSTART;VALUE=DATE-TIME:20210625T100000Z
DTEND;VALUE=DATE-TIME:20210625T110000Z
DTSTAMP;VALUE=DATE-TIME:20230921T160806Z
UID:SeminarioGeometry/15
DESCRIPTION:Title: Classification of non-collapsed translators in \\(\\mathbb{R}^4
\\)\nby Or Hershkovits (Hebrew University of Jerusalem) as part of Geo
metry Seminar\, Universidad de Granada (Spain)\n\n\nAbstract\nTranslating
solution to the mean curvature flow form\, together with self-shrinking so
lutions\, the most important class of singularity models of the flow. When
a translator arises as a blow-up of a mean convex mean curvature flow\, i
t also naturally satisfies a non-collapsness condition.\nIn this talk\, I
will report on a recent work with Kyeongsu Choi and Robert Haslhofer\, in
which we show that every mean convex\, non-collapsed\, translator in $\\ma
thbb{R}^4$ is a member of a one parameter family of translators\, which wa
s earlier constructed by Hoffman\, Ilmanen\, Martín and White.\n
LOCATION:https://researchseminars.org/talk/SeminarioGeometry/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Kalaj (University of Montenegro)
DTSTART;VALUE=DATE-TIME:20211001T100000Z
DTEND;VALUE=DATE-TIME:20211001T110000Z
DTSTAMP;VALUE=DATE-TIME:20230921T160806Z
UID:SeminarioGeometry/16
DESCRIPTION:Title: Curvature of minimal graphs\nby David Kalaj (University of
Montenegro) as part of Geometry Seminar\, Universidad de Granada (Spain)\n
\n\nAbstract\nWe consider the Gaussian curvature conjecture of a minimal g
raph $S$ over the unit disk. First of all we reduce the general conjecture
to the estimating the Gaussian curvature of some Scherk's type minimal su
rfaces over a quadrilateral inscribed in the unit disk containing the or
igin inside.\nAs an application we improve so far the obtained upper estim
ates of Gaussian curvature at the point above the center. Further we obt
ain an optimal estimate of the Gaussian curvature at the point $\\mathbf{w
}$ over the center of the disk\, provided $\\mathbf{w}$ satisfies certain
"symmetric" conditions. The result extends a classical result of Finn and
Osserman in 1964. In order to do so\, we construct a certain family $S^t$\
, $t\\in[t_\\circ\, \\pi/2]$ of Scherk's type minimal graphs over the isos
celes trapezoid inscribed in the unit disk. Then we compare the Gaussian c
urvature of the graph $S$ with that of $S^t$ at the point $\\mathbf{w}$ ov
er the center of the disk.\n
LOCATION:https://researchseminars.org/talk/SeminarioGeometry/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Álvaro Kruger Ramos (Universidade Federal do Rio Grande do Sul)
DTSTART;VALUE=DATE-TIME:20211015T100000Z
DTEND;VALUE=DATE-TIME:20211015T110000Z
DTSTAMP;VALUE=DATE-TIME:20230921T160806Z
UID:SeminarioGeometry/17
DESCRIPTION:Title: Area Minimizing Surfaces in $E(-1\,\\tau)$\nby Álvaro Krug
er Ramos (Universidade Federal do Rio Grande do Sul) as part of Geometry S
eminar\, Universidad de Granada (Spain)\n\n\nAbstract\nRecall that $E(-1\,
\\tau)$ is a homogeneous space with four-dimensional isometry group which
is given by the total space of a fibration over $\\mathbb{H}^2$ with bundl
e curvature $\\tau$. Given a finite collection of simple closed curves $\\
Gamma$ in its asymptotic boundary\, we provide sufficient conditions on $\
\Gamma$ so that there exists an area minimizing surface $\\Sigma$ in $E(-1
\,\\tau)$ with asymptotic boundary $\\Gamma$. We also present necessary co
nditions for such a surface $\\Sigma$ to exist. This is joint work with P.
Klaser and A. Menezes.\n
LOCATION:https://researchseminars.org/talk/SeminarioGeometry/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giuseppe Pipoli
DTSTART;VALUE=DATE-TIME:20211105T110000Z
DTEND;VALUE=DATE-TIME:20211105T120000Z
DTSTAMP;VALUE=DATE-TIME:20230921T160806Z
UID:SeminarioGeometry/18
DESCRIPTION:Title: Constant mean curvature hypersurfaces in $\\mathbb{H}^n \\times
\\mathbb{R}$ with small planar boundary\nby Giuseppe Pipoli as part of
Geometry Seminar\, Universidad de Granada (Spain)\n\n\nAbstract\nWe show
that constant mean curvature hypersurfaces in $\\mathbb{H}^n \\times\\math
bb{R}$\, with small and pinched boundary contained in a horizontal slice $
P$ are topological disks\, provided they are contained in one of the two h
alfspaces determined by $P$. This is a joint work with B. Nelli and it is
the analogous in $\\mathbb{H}^n \\times\\mathbb{R}$ of a result in $\\math
bb{R}^3$ by A. Ros and H. Rosenberg.\n
LOCATION:https://researchseminars.org/talk/SeminarioGeometry/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antonio Martínez-Triviño (Universidad de Granada)
DTSTART;VALUE=DATE-TIME:20220204T110000Z
DTEND;VALUE=DATE-TIME:20220204T120000Z
DTSTAMP;VALUE=DATE-TIME:20230921T160806Z
UID:SeminarioGeometry/19
DESCRIPTION:Title: A Weiertrass type representation for translating solitons and s
ingular minimal surfaces\nby Antonio Martínez-Triviño (Universidad d
e Granada) as part of Geometry Seminar\, Universidad de Granada (Spain)\n\
nLecture held in Sala de Conferencias (IMAG).\n\nAbstract\nIn this talk\,
we present a Weierstrass representation formula for translating solitons a
nd singular minimal surfaces in $\\mathbb{R}^3$. As application\, we study
when the euclidean Gauss map has harmonic argument and solve a general Ca
uchy's problem in this class of surfaces.\n
LOCATION:https://researchseminars.org/talk/SeminarioGeometry/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlos Shahbazi (Universidad Autónoma de Madrid)
DTSTART;VALUE=DATE-TIME:20220318T110000Z
DTEND;VALUE=DATE-TIME:20220318T120000Z
DTSTAMP;VALUE=DATE-TIME:20230921T160806Z
UID:SeminarioGeometry/20
DESCRIPTION:Title: The mathematical theory of globally hyperbolic supersymmetric c
onfigurations in supergravity\nby Carlos Shahbazi (Universidad Autóno
ma de Madrid) as part of Geometry Seminar\, Universidad de Granada (Spain)
\n\nLecture held in Seminario 1 (IMAG).\n\nAbstract\nI will give a pedagog
ical introduction to the incipient mathematical theory of globally hyperbo
lic supersymmetric configurations in supergravity in four dimensions. Firs
t\, I will introduce the basics of supergravity in four dimensions as well
as the notion of globally supersymmetric configuration as a solution to t
he supergravity spinorial equations. Then\, I will introduce the theory of
spinorial polyforms associated to bundles of irreducible real Clifford mo
dules\, which provides a convenient geometric framework to study first-ord
er differential spinorial equations\, such as the supergravity spinorial e
quations. Then\, I will consider the evolution problem for globally hyperb
olic supersymmetric configurations\, focusing on the constraint equations\
, their moduli of solutions\, and the construction of explicit solutions t
o the evolution equations\, which we reformulate as the supergravity flow
equations for a coupled family of functions and global co-frames on a Cauc
hy hypersurface. This will lead us to explore in detail the case of (possi
bly Einstein) globally hyperbolic Lorentzian four-manifolds equipped with
a parallel or Killing spinor\, obtaining several results about the differe
ntiable topology and geometry of such manifolds. Finally\, I will mention
several open problems and open directions for future research.\n
LOCATION:https://researchseminars.org/talk/SeminarioGeometry/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gioacchino Antonelli (Scuola Normale Superiore di Pisa)
DTSTART;VALUE=DATE-TIME:20220218T110000Z
DTEND;VALUE=DATE-TIME:20220218T120000Z
DTSTAMP;VALUE=DATE-TIME:20230921T160806Z
UID:SeminarioGeometry/21
DESCRIPTION:Title: Sharp differential inequalities for the isoperimetric profile i
n spaces with Ricci lower bounds\nby Gioacchino Antonelli (Scuola Norm
ale Superiore di Pisa) as part of Geometry Seminar\, Universidad de Granad
a (Spain)\n\nLecture held in Seminar 1\, IMAG.\n\nAbstract\nIn this talk I
will discuss sharp differential inequalities for the isoperimetric profil
e function in spaces with Ricci bounded from below\, and with volumes of u
nit balls uniformly bounded from below. After that\, I will highlight some
of the consequences of such inequalities for the isoperimetric problem. A
fter a short introduction about the notion of perimeter in the metric meas
ure setting\, I will pass to the motivation and statement of the sharp dif
ferential inequalities on Riemannian manifolds. Hence\, I will discuss the
proof\, which builds on a non smooth generalized existence theorem for th
e isoperimetric problem (after Ritoré-Rosales\, and Nardulli)\, and on a
non smooth sharp Laplacian comparison theorem for the distance function fr
om isoperimetric boundaries (after Mondino-Semola). At the end I will disc
uss how to use such differential inequalities to study the behaviour of th
e isoperimetric profile for small volumes. This talk is based on some resu
lts that recently appeared in a work in collaboration with E. Pasqualetto\
, M. Pozzetta\, and D. Semola. Some of the tools and ideas exploited for t
he proofs come from other works in collaboration with E. Bruè\, M. Fogagn
olo\, and S. Nardulli.\n
LOCATION:https://researchseminars.org/talk/SeminarioGeometry/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Franc Forstneric (University of Ljubljana)
DTSTART;VALUE=DATE-TIME:20220401T100000Z
DTEND;VALUE=DATE-TIME:20220401T110000Z
DTSTAMP;VALUE=DATE-TIME:20230921T160806Z
UID:SeminarioGeometry/22
DESCRIPTION:Title: Hyperbolic domains in real Euclidean spaces\nby Franc Forst
neric (University of Ljubljana) as part of Geometry Seminar\, Universidad
de Granada (Spain)\n\nLecture held in Seminar 1 (IMAG).\n\nAbstract\nIn a
recent joint work with David Kalaj (2021)\, we introduced a new Finsler ps
eudometric on any domain in the real Euclidean space $\\mathbb R^n$ for $n
\\ge 3$\, defined in terms of conformal harmonic discs\, by analogy with t
he Kobayashi pseudometric on complex manifolds. This "minimal pseudometric
" describes the maximal rate of growth of hyperbolic conformal minimal sur
faces in a given domain. On the unit ball\, the minimal metric coincides w
ith the classical Beltrami-Cayley-Klein metric. I will discuss sufficient
geometric conditions for a domain to be (complete) hyperbolic\, meaning th
at its minimal pseudometric is a (complete) metric.\n
LOCATION:https://researchseminars.org/talk/SeminarioGeometry/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hao Chen
DTSTART;VALUE=DATE-TIME:20220603T100000Z
DTEND;VALUE=DATE-TIME:20220603T110000Z
DTSTAMP;VALUE=DATE-TIME:20230921T160806Z
UID:SeminarioGeometry/23
DESCRIPTION:Title: Triply periodic minimal surfaces\nby Hao Chen as part of Ge
ometry Seminar\, Universidad de Granada (Spain)\n\nLecture held in Seminar
1 (IMAG).\n\nAbstract\nTriply periodic minimal surfaces (TPMSs) are minim
al surfaces in flat 3-tori. I will review recent discoveries of new exampl
es of TPMSs and outline future steps towards an eventual complete classifi
cation of TPMSs of genus 3.\n
LOCATION:https://researchseminars.org/talk/SeminarioGeometry/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hao Chen
DTSTART;VALUE=DATE-TIME:20220606T100000Z
DTEND;VALUE=DATE-TIME:20220606T110000Z
DTSTAMP;VALUE=DATE-TIME:20230921T160806Z
UID:SeminarioGeometry/24
DESCRIPTION:Title: Gluing Karcher-Scherk saddle towers\nby Hao Chen as part of
Geometry Seminar\, Universidad de Granada (Spain)\n\nLecture held in Semi
nar 1 (IMAG).\n\nAbstract\nTraizet’s node opening technique has been ver
y powerful to construct minimal surfaces. In fact\, it was first applied t
o glue saddle towers into minimal surfaces. But for technical reasons\, th
e construction has much room to improve. I will talk about the ongoing pro
ject that addresses to various technical problems in the gluing constructi
on. In particular\, careful treatment of Dehn twist has revealed very subt
le interactions between saddle towers.\n
LOCATION:https://researchseminars.org/talk/SeminarioGeometry/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hao Chen
DTSTART;VALUE=DATE-TIME:20220609T100000Z
DTEND;VALUE=DATE-TIME:20220609T110000Z
DTSTAMP;VALUE=DATE-TIME:20230921T160806Z
UID:SeminarioGeometry/25
DESCRIPTION:Title: Minimal surfaces as an interdisciplinary topic\nby Hao Chen
as part of Geometry Seminar\, Universidad de Granada (Spain)\n\nLecture h
eld in Semianr 2 (IMAG).\n\nAbstract\nAll my works on minimal surfaces has
been motivated or inspired by natural sciences\, including material scien
ces\, bio-membranes\, fluid dynamics\, etc. I will give an informal talk (
since I’m not natural scientist) about how minimal surface theory could
benefit from interdisciplinary interactions.\n
LOCATION:https://researchseminars.org/talk/SeminarioGeometry/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adrià Marín Salvador
DTSTART;VALUE=DATE-TIME:20220624T100000Z
DTEND;VALUE=DATE-TIME:20220624T110000Z
DTSTAMP;VALUE=DATE-TIME:20230921T160806Z
UID:SeminarioGeometry/26
DESCRIPTION:Title: On the canonical contact structure of the space of null geodesi
cs of a spacetime: the role of Engel geometry in dimension 3\nby Adri
à Marín Salvador as part of Geometry Seminar\, Universidad de Granada (S
pain)\n\nLecture held in Seminar 1 (IMAG).\n\nAbstract\nThe space of null
geodesics of a spacetime (a Lorentzian manifold with a choice of future) s
ometimes has the structure of a smooth manifold. When this is the case\, i
t comes equipped with a canonical contact structure. I will introduce the
theory for a countable number of metrics on the product $S^2\\times S^$. M
otivated by these examples\, I will comment on how Engel geometry can be u
sed to describe the manifold of null geodesics\, by considering the Cartan
deprolongation of the Lorentz prolongation of the spacetime. This allows
us to characterize the 3-contact manifolds which are spaces of null geodes
ics\, and to retrieve the spacetime they come from. This is joint work wit
h R. Rubio.\n
LOCATION:https://researchseminars.org/talk/SeminarioGeometry/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eduardo Longa (Universidade de Sao Paulo)
DTSTART;VALUE=DATE-TIME:20220615T100000Z
DTEND;VALUE=DATE-TIME:20220615T110000Z
DTSTAMP;VALUE=DATE-TIME:20230921T160806Z
UID:SeminarioGeometry/27
DESCRIPTION:Title: Critical embeddings for the first eigenvalue of the Laplacian\nby Eduardo Longa (Universidade de Sao Paulo) as part of Geometry Semin
ar\, Universidad de Granada (Spain)\n\nLecture held in Seminar 1 (IMAG).\n
\nAbstract\nThe eigenvalues of the Laplace-Beltrami operator on a closed R
iemannian manifold are very natural geometric invariants. Although in many
problems the Riemannian structure is kept fixed\, the eigenvalues can be
seen as functionals in the space of metrics. This is the suitable setting
for the calculus of variations. In this vein\, El Soufi and Ilias have cha
racterised the metrics which are critical for the first eigenvalue among a
ll metrics of fixed volume and among all metrics of fixed volume in a conf
ormal class. In the talk\, I will prove a similar characterisation for som
e critical metrics which are induced by embeddings into a fixed Riemannian
manifold.\n
LOCATION:https://researchseminars.org/talk/SeminarioGeometry/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Handan Yildirim (University of Istanbul)
DTSTART;VALUE=DATE-TIME:20220708T100000Z
DTEND;VALUE=DATE-TIME:20220708T110000Z
DTSTAMP;VALUE=DATE-TIME:20230921T160806Z
UID:SeminarioGeometry/28
DESCRIPTION:Title: On Legendrian dual surfaces of a spacelike curve in the 3-dimen
sional lightcone\nby Handan Yildirim (University of Istanbul) as part
of Geometry Seminar\, Universidad de Granada (Spain)\n\nLecture held in Se
minar 1 (IMAG).\n\nAbstract\nIn this talk which is based on the joint work
with Kentaro Saji given in [3]\, taking into account the Legendrian duali
ties in [2] which are extensions of the Legendrian dualities in [1]\, we f
irst introduce new extended Legendrian dualities for the 3-dimensional pse
udo-spheres of various radii in Lorentz-Minkowski 4-space. Secondly\, by c
onnecting all of these Legendrian dualities continuously\, we construct Le
gendrian dual surfaces (lying in these 3-dimensional pseudo-spheres) of a
spacelike curve in the 3-dimensional lightcone. Finally\, we investigate t
he singularities of these surfaces and show the dualities of the singulari
ties of a certain class of such a surface in the 3-dimensional lightcone.\
n\n[1] S. Izumiya\, Legendrian dualities and spacelike hypersurfaces in th
e lightcone\, Moscow Mathematical Journal\, 9 (2009)\, 325-357.\n\n[2] S.
Izumiya\, H. Yildirim\, Extensions of the mandala of Legendrian dualities
for pseudo-spheres in Lorentz-Minkowski space\, Topology and its Applicati
ons\, 159(2012)\, 509-518.\n\n[3] K. Saji\, H. Yildirim\, Legendrian dual
surfaces of a spacelike curve in the 3-dimensional lightcone\, Journal of
Geometry and Physics\, 104593\, https://doi.org/10.1016/j.geomphys.2022.10
4593\n
LOCATION:https://researchseminars.org/talk/SeminarioGeometry/28/
END:VEVENT
END:VCALENDAR