Infinitesimal structure of differentiability spaces, and metric differentiation. (English) Zbl 1360.30047
Summary: We prove metric differentiation for differentiability spaces in the sense of Cheeger [D. Bate, J. Am. Math. Soc. 28, No. 2, 421–482 (2015; Zbl 1307.30097); J. Cheeger, Geom. Funct. Anal. 9, No. 3, 428–517 (1999; Zbl 0942.58018); S. Keith, Adv. Math. 183, No. 2, 271–315 (2004; Zbl 1077.46027)]. As corollaries we give a new proof of one of the main results of [Zbl 0942.58018], a proof that the Lip-lip constant of any Lip-lip space in the sense of Keith [Zbl 1077.46027)] is equal to 1, and new nonembeddability results.
Keywords:
metric measure space; bi-Lipschitz embedding; measurable differentiable structure; differentiability space; metric differentiationReferences:
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