Existence of Anisotropic Minkowski Content
Classical Analysis and ODEs
2026-05-12 v5
Abstract
This paper is devoted to the existence of anisotropic Minkowski content and anisotropic outer Minkowski content. Our result is that the Minkowski content of the topological boundary of a given set of finite perimeter coincides with the perimeter of if and only if the anisotropic Minkowski content of the topological boundary of coincides with half of the sum of the anisotropic perimeter of and the anisotropic perimeter of the complement of As a consequence, we find that the existence of anisotropic outer Minkowski content of a given set of finite perimeter and its complement ensures the existence of outer Minkowski content of the set and its complement.
Keywords
Cite
@article{arxiv.2508.08156,
title = {Existence of Anisotropic Minkowski Content},
author = {Filip Fryš},
journal= {arXiv preprint arXiv:2508.08156},
year = {2026}
}