On the differentiability of lipschitz maps from metric measure spaces to banach spaces

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

We consider metric measure spaces satisfing a doubling condition and a Poincaré inequality in the upper gradient sense. We show that the results of [Che99] on differentiability of real valued Lipschitz functions and the resulting bi-Lipschitz nonembedding theorems for finite dimensional vector space targets extend to Banach space targets having what we term a good finite dimensional approximation. This class of targets includes separable dual spaces. We also observe that there is a straightforward extension of Pansu’s differentiation theory for Lipschitz maps between Carnot groups, [Pan89], to the most general possible class of Banach space targets, those with the Radon-Nikodym property.

Original languageEnglish (US)
Title of host publicationInspired By S S Chern
Subtitle of host publicationA Memorial Volume In Honor Of A Great Mathematician
PublisherWorld Scientific Publishing Co.
Pages129-152
Number of pages24
ISBN (Electronic)9789812772688
DOIs
StatePublished - Jan 1 2006

ASJC Scopus subject areas

  • Mathematics(all)

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