Perimeter as relaxed Minkowski content in metric measure spaces

TL;DR

This paper establishes that in general metric measure spaces, the perimeter of a set equals the relaxed Minkowski content, linking geometric measure theory concepts in a broad setting.

Contribution

It proves the equivalence of perimeter and relaxed Minkowski content in general metric measure spaces, extending classical results beyond Euclidean spaces.

Findings

Perimeter equals relaxed Minkowski content in metric measure spaces

Provides a new characterization of perimeter in non-Euclidean settings

Extends geometric measure theory results to general metric measure spaces

Abstract

In this note we prove that on general metric measure spaces the perimeter is equal to the relaxation of the Minkowski content w.r.t.\ convergence in measure