A note on indecomposable sets of finite perimeter

TL;DR

This paper demonstrates that the decomposition theorem for sets of finite perimeter into indecomposable components, previously proven under an isotropicity condition in metric spaces, holds without this assumption, broadening its applicability.

Contribution

The authors remove the isotropicity condition from the decomposition theorem for finite perimeter sets in metric spaces, extending the theorem's validity.

Findings

Decomposition theorem holds without isotropicity condition

Applicable in broader classes of metric spaces

Supports analysis of finite perimeter sets in general metric spaces

Abstract

Bonicatto--Pasqualetto--Rajala (2020) proved that a decomposition theorem for sets of finite perimeter into indecomposable sets, known to hold in Euclidean spaces, holds also in complete metric spaces equipped with a doubling measure, supporting a Poincar\'e inequality, and satisfying an \emph{isotropicity} condition. We show that the last assumption can be removed.