# Global Lipschitz extension preserving local constants

created by gigli on 21 Jul 2020

[BibTeX]

preprint

Inserted: 21 jul 2020

Year: 2020

ArXiv: 2007.10011 PDF

Abstract:

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.

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