Calculus of Variations and Geometric Measure Theory

L. Ambrosio - N. Gigli - S. Di Marino

Perimeter as relaxed Minkowski content in metric measure spaces

created by ambrosio on 04 Mar 2016
modified by dimarino on 24 Jul 2018


Submitted Paper

Inserted: 4 mar 2016
Last Updated: 24 jul 2018

Journal: Nonlinear Analysis: Theory, Methods & Applications
Volume: 153
Pages: 78-88
Year: 2016
Doi: 10.1016/

ArXiv: 1603.08412 PDF


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