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