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arXiv · 2007.10011

Global Lipschitz extension preserving local constants

Simone Di Marino·Nicola Gigli·Aldo Pratelli
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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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Simone Di Marino, Nicola Gigli, Aldo Pratelli. 2020-07-20. Global Lipschitz extension preserving local constants. https://arxiv.org/abs/2007.10011

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