# zbMATH — the first resource for mathematics

Uniqueness of the Cheeger set of a convex body. (English) Zbl 1221.35171
Summary: We prove that if $$C \subset \mathbb R^N$$ is of class $$C^2$$and uniformly convex, the Cheeger set of $$C$$ is unique. The Cheeger set of $$C$$ is the set that minimizes, inside $$C$$, the ratio of perimeter over volume.

##### MSC:
 35J70 Degenerate elliptic equations 49J40 Variational inequalities 52A20 Convex sets in $$n$$ dimensions (including convex hypersurfaces)
##### Keywords:
convex bodies; variational problems
Full Text: