Uniqueness of the Cheeger set of a convex body

By V. Caselles, Antonin Chambolle, Matteo Novaga. Pacific Journal of Mathematics, 2007

130 citations recorded by the source corpus.

Abstract We prove that if C ⊂ R N is 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 .

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/05964a4c50beabba8aed574b49366cce81b140cd

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

The volume preserving crystalline mean curvature flow of convex sets in R^N (2009, unknown): “For μ = μ∗, (65) has at least two solution, ∅ and the convex set {uλ = ‖uλ‖∞}, while it has been shown in [15, 2] that, at least in the isotropic case φ(·) = |·|, there is no other solution.”
AN INTRODUCTION TO THE CHEEGER PROBLEM (2011, unknown): “[1] F.”
Nonlocal perimeter, curvature and minimal surfaces for measurable sets (2019, background): “Furthermore, in [3] it is proved that there is a unique Cheeger set inside any non–trivial convex body in R , being this Cheeger set convex.”
A characterization of convex calibrable sets in RN with respect to anisotropic norms (2008, background): “In higher dimension, uniqueness (hence convexity) of the Cheeger set of a convex set C ⊆ R has been recently proved by [24,1].”
On the Cheeger sets in strips and non-convex domains (2014, background): “The first property, which can be found in [1] (see also the references therein), is the following uniqueness and convexity result.”