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SUMMARY:Theodora Bourni (University of Tennessee Knoxville)
DTSTART:20210504T143000Z
DTEND:20210504T153000Z
DTSTAMP:20260422T225717Z
UID:GALSeminar/1
DESCRIPTION:Title: Ancient solutions to mean curvature flow\nby Theodora Bourni (Unive
rsity of Tennessee Knoxville) as part of Geometric Analysis in the Large\n
\n\nAbstract\nMean curvature flow (MCF) is the gradient flow of the area f
unctional\; it moves the surface in the direction of steepest decrease of
area. An important motivation for the study of MCF comes from its potenti
al geometric applications\, such as classification theorems and geometric
inequalities. MCF develops “singularities” (curvature blow-up)\, which
obstruct the flow from existing for all times and therefore understanding
these high curvature regions is of great interest. This is done by study
ing ancient solutions\, solutions that have existed for all times in the p
ast\, and which model singularities. In this talk we will discuss their im
portance and ways of constructing and classifying such solutions. In parti
cular\, we will focus on “collapsed” solutions and construct\, in all
dimensions n>=2\, a large family of new examples\, including both symmetri
c and asymmetric examples\, as well as many eternal examples that do not e
volve by translation. Moreover\, we will show that collapsed solutions de
compose “backwards in time” into a canonical configuration of Grim hyp
erplanes which satisfies certain necessary conditions. This is joint work
with Mat Langford and Giuseppe Tinaglia.\n
LOCATION:https://researchseminars.org/talk/GALSeminar/1/
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SUMMARY:Barbara Nelli (Università dell’Aquila)
DTSTART:20210511T143000Z
DTEND:20210511T153000Z
DTSTAMP:20260422T225717Z
UID:GALSeminar/2
DESCRIPTION:Title: Hypersurfaces with constant higher order mean curvature\nby Barbara
Nelli (Università dell’Aquila) as part of Geometric Analysis in the La
rge\n\n\nAbstract\nWe give an overview of some old and new results about t
he shape of hypersurfaces whose one of the symmetric functions of the prin
cipal curvature is constant.\n
LOCATION:https://researchseminars.org/talk/GALSeminar/2/
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SUMMARY:Laurent Mazet (Université de Tours)
DTSTART:20210518T143000Z
DTEND:20210518T153000Z
DTSTAMP:20260422T225717Z
UID:GALSeminar/3
DESCRIPTION:Title: Rigidity of Riemannian manifolds containing an equator\nby Laurent
Mazet (Université de Tours) as part of Geometric Analysis in the Large\n\
n\nAbstract\nIf a Riemannian sphere S^2 with curvature between 0 and 1 has
a closed geodesic of length 2\\pi\, then its curvature is constant and eq
ual to 1. This result is due to Calabi. In dimension 3 and under the same
curvature assumptions\, the existence of a minimal sphere of area 4\\pi ri
gidifies the metric. This result has been obtained in a preceding work wit
h H. Rosenberg. In this talk\, I will explain how this work can be general
ized in higher dimension. As a consequence\, I will also give a rigidity r
esult concerning Simon-Smith width.\n
LOCATION:https://researchseminars.org/talk/GALSeminar/3/
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SUMMARY:Ezequiel Barbosa (Universidad de Granada / Universidade Federal de
Minas Gerais)
DTSTART:20210525T143000Z
DTEND:20210525T153000Z
DTSTAMP:20260422T225717Z
UID:GALSeminar/4
DESCRIPTION:Title: Some characterization results of the Delaunay Surfaces\nby Ezequiel
Barbosa (Universidad de Granada / Universidade Federal de Minas Gerais) a
s part of Geometric Analysis in the Large\n\n\nAbstract\nIn this talk we w
ill discuss some new characterization results of some Delaunay capillary s
urfaces in a Euclidean ball.\n
LOCATION:https://researchseminars.org/talk/GALSeminar/4/
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SUMMARY:Marco Guaraco (Imperial College London)
DTSTART:20210601T143000Z
DTEND:20210601T153000Z
DTSTAMP:20260422T225717Z
UID:GALSeminar/5
DESCRIPTION:Title: Mean curvature flow in homology and foliations of hyperbolic 3-manifold
s\nby Marco Guaraco (Imperial College London) as part of Geometric Ana
lysis in the Large\n\n\nAbstract\nWe will discuss global aspects and appli
cations of the mean curvature flow and min-max in closed manifolds. Topics
include: non-separating hypersurfaces with non-vanishing mean curvature\,
incompressible surfaces\, existence of monotone isotopies towards stable
minimal surfaces\, foliations of hyperbolic 3-manifolds and outermost mini
mal surfaces in quasi-Fuchsian ends. This is a joint work with Vanderson L
ima and Franco Vargas Pallete.\n
LOCATION:https://researchseminars.org/talk/GALSeminar/5/
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SUMMARY:José Espinar (Universidad de Cádiz)
DTSTART:20210608T143000Z
DTEND:20210608T153000Z
DTSTAMP:20260422T225717Z
UID:GALSeminar/6
DESCRIPTION:Title: On non-compact free boundary minimal hypersurfaces in the Riemannian Sc
hwarzschild spaces\nby José Espinar (Universidad de Cádiz) as part o
f Geometric Analysis in the Large\n\n\nAbstract\nWe will show that\, in co
ntrast with the 3-dimensional case\, the Morse index of a free boundary ro
tationally symmetric totally geodesic hypersurface of the n-dimensional Ri
emannnian Schwarzschild space with respect to variations that are tangenti
al along the horizon is zero\, for n≥4. Moreover\, we will show that the
re exist non-compact free boundary minimal hypersurfaces which are not tot
ally geodesic\, n≥8\, with Morse index equal to zero. Also\, for n≥4\,
there exist infinitely many non-compact free boundary minimal hypersurfac
es\, which are not congruent to each other\, with infinite Morse index.\n
LOCATION:https://researchseminars.org/talk/GALSeminar/6/
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