Calculus of Variations and Geometric Measure Theory

S. Di Marino - N. Gigli - A. Pratelli

Global Lipschitz extension preserving local constants

created by gigli on 21 Jul 2020
modified by pratelli on 20 Jan 2022


Published Paper

Inserted: 21 jul 2020
Last Updated: 20 jan 2022

Journal: Rend. Lincei Mat. Appl.
Year: 2020

ArXiv: 2007.10011 PDF


The intent of this short note is to extend real valued Lipschitz functions on metric spaces, while locally preserving the asymptotic Lipschitz constant. We then apply this results to give a simple and direct proof of the fact that Sobolev spaces on metric measure spaces defined with a relaxation approach \`a la Cheeger are invariant under isomorphism class of mm-structures.