# Uniqueness of the Cheeger set of a convex body

created by novaga on 06 Apr 2006
modified on 10 Nov 2018

[BibTeX]

Published Paper

Inserted: 6 apr 2006
Last Updated: 10 nov 2018

Journal: Pacific Journal of Mathematics
Volume: 232
Number: 1
Pages: 77-90
Year: 2007

Abstract:

We prove that if $C \subset \mathbb R^N$ is of class $C^2$ 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.