Global Lipschitz extension preserving local constants (2007.10011v1)

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.