Inserted: 6 apr 2006
Last Updated: 10 nov 2018
Journal: Pacific Journal of Mathematics
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.