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Title: Uniqueness of the Cheeger set of a convex body
Year: 08/2007
Language: English
Abstract: We prove that if C is a convex N-dimensional body whose boundary is twice continuously differentiable and uniformly convex, then the Cheeger set of C is unique. The Cheeger set of C is the set which minimizes, inside C, the ratio perimeter over volume.

This is a revised version (of July 2006) of a paper submitted in April 2006, to appear in Pacific Journal of Mathematics (231 n°2, 2007)

A recent proof of uniqueness of the Cheeger set without any regularity assumption on the boundary of the convex body has been found by Alter and Caselles (see http://www.iua.upf.es/~vcaselles/, the preprint though seems yet unavailable)
Pages: 13
MSC: 52-99 52A39
Download: 621.pdf
URL: www.cmap.polytechnique.fr/~antonin
Auteurs:V. Caselles
Auteurs:A. Chambolle
Auteurs:M. Novaga
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