Isoperimetric inequalities in Euclidean convex bodies

In this paper we consider the problem of minimizing the relative perimeter under a volume constraint in the interior of a convex body, i.e., a compact convex set in Euclidean space with interior points. We shall not impose any regularity assumption on the boundary of the convex set. Amongst other results, we shall prove the equivalence between Hausdorff and Lipschitz convergence, the continuity of the isoperimetric profile with respect to the Hausdorff distance, and the convergence in Hausdorff distance of sequences of isoperimetric regions and their free boundaries. We shall also describe the behavior of the isoperimetric profile for small volume, and the behavior of isoperimetric regions for small volume.

• Publication year

  2013

• Venue

  Transactions of the American Mathematical Society

• Publication date

  2013-02-19

• Fields of study

  Mathematics

• Identifiers
  DOI 10.1090/S0002-9947-2015-06197-2arXiv 1302.4588
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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