On maximal Cheeger sets

Abstract

In this paper, we consider a constrained weighted total variation minimization problem, which is motivated by landslide modeling and may be viewed as a relaxation of a generalized Cheeger problem. We prove that level sets of minimizers are generalized Cheeger sets and obtain qualitative properties of the minimizers: they are all bounded and all achieve their essential supremum on a set of positive measures. We then propose a method to find the maximal Cheeger sets and give numerical computations.