23.04.2015, 16:15 Uhr  –  Universität Potsdam, Neues Palais, Haus 9, Raum 115
Seminar "Topics in Geometric Analysis"

Manuel Ritore and Julian Scheuer

16:15 Uhr Manuel Ritore (Granada) Isoperimetric inequalities in unbounded convex bodies

I shall consider the problem of minimizing the relative perimeter under a volume constraint in the interior of an unbounded convex body with arbitrary boundary. I shall give an example of a convex body whose isoperimetric profile is identically zero and give a characterization of the convex bodies with positive isoperimetric profile in terms of their asymptotic cylinders. I shall also show existence of isoperimetric regions in a generalized sense, and prove the concavity of the function I^{(n+1)/n}, where I is the isoperimetric profile and R^{n+1} is the ambient Euclidean space.
This is joint work in progress with Gian Paolo Leonardi and Efstratios Vernadakis.

 
17:45 Uhr Julian Scheuer (Freiburg) Explicit rigidity for almost-umbilical hypersurfaces

Abstract

 
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