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arXiv · 1503.07348

Infinitesimal structure of differentiability spaces, and metric differentiation

Jeff Cheeger·Bruce Kleiner·Andrea Schioppa
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Abstract

We prove metric differentiation for differentiability spaces in the sense of Cheeger. As corollaries we give a new proof that the minimal generalized upper gradient coincides with the pointwise Lipschitz constant for Lipschitz functions on PI spaces, a proof that the Lip-lip constant of any Lip-lip space in the sense of Keith is equal to $1$, and new nonembeddability results.

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Jeff Cheeger, Bruce Kleiner, Andrea Schioppa. 2015-03-25. Infinitesimal structure of differentiability spaces, and metric differentiation. https://arxiv.org/abs/1503.07348

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