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SUMMARY:Costante Bellettini (University College London)
DTSTART:20220720T120000Z
DTEND:20220720T140000Z
DTSTAMP:20260423T005832Z
UID:NCTS-GMT/11
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NCTS-GMT/11/
 ">Hypersurfaces with prescribed-mean-curvature: existence and properties</
 a>\nby Costante Bellettini (University College London) as part of NCTS int
 ernational Geometric Measure Theory seminar\n\n\nAbstract\nLet $N$ be a co
 mpact Riemannian manifold of dimension $3$ or higher\, and $g$ a Lipschitz
  non-negative (or non-positive) function on $N$.  In joint works with Nesh
 an Wickramasekera we prove that there exists a closed hypersurface $M$ who
 se mean curvature attains the values prescribed by $g$.  Except possibly f
 or a small singular set (of codimension $7$ or higher)\, the hypersurface 
 $M$ is $C^2$ immersed and two-sided (it admits a global unit normal)\; the
  scalar mean curvature at $x$ is $g(x)$ with respect to a global choice of
  unit normal. More precisely\, the immersion is a quasi-embedding\, namely
  the only non-embedded points are caused by tangential self-intersections:
  around any such non-embedded point\, the local structure is given by two 
 disks\, lying on one side of each other\, and intersecting tangentially (a
 s in the case of two spherical caps touching at a point). A special case o
 f PMC (prescribed-mean-curvature) hypersurfaces is obtained when $g$ is a 
 constant\, in which the above result gives a CMC (constant-mean-curvature)
  hypersurface for any prescribed value of the mean curvature.\n\nGet-toget
 her (30 min) $\\cdot$ presentation Costante Bellettini (60 min) $\\cdot$ q
 uestions and discussions (30 min).\n
LOCATION:https://researchseminars.org/talk/NCTS-GMT/11/
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