Citation:Alter F, Caselles V. Uniqueness of the cheeger set of a convex body. Nonlinear Anal Theory Methods Appl. 2009 Jan;70(1):32-44. DOI: 10.1016/j.na.2007.11.032
We prove that if C C RN 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.