Calculus of Variations and Geometric Measure Theory
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F. Alter - V. Caselles

Uniqueness of the Cheeger set of a convex body

created by caselles on 09 Oct 2007


Submitted Paper

Inserted: 9 oct 2007

Journal: Nonlinear Analysis TMA
Year: 2007


We prove that if $C \subset \R^N$ is a an open bounded convex set, then there is only one Cheeger set inside $C$ and it is convex. A Cheeger set of $C$ is a set which minimizes the ratio perimeter over volume among all subsets of $C$.

Keywords: Cheeger sets


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