Infinitesimal Structure of Differentiability Spaces, and Metric Differentiation

Infinitesimal Structure of Differentiability Spaces, and Metric Differentiation

We prove metric differentiation for differentiability spaces in the sense of Cheeger [10, 14, 27]. As corollarieswe give a new proof of one of the main results of [14], a proof that the Lip-lip constant of any Lip-lip space in the sense of Keith [27] is equal to 1, and new nonembeddability results.

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Veröffentlicht in:Analysis and Geometry in Metric Spaces 2016-01, Vol.4 (1)
Hauptverfasser: Cheeger, Jeff, Kleiner, Bruce, Schioppa, Andrea
Format: Artikel
Sprache:eng
Schlagworte:
bi-Lipschitz embedding
differentiability space
Differentiation
measurable differentiable structure
metric differentiation
Metric measure space
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Zusammenfassung:We prove metric differentiation for differentiability spaces in the sense of Cheeger [10, 14, 27]. As corollarieswe give a new proof of one of the main results of [14], a proof that the Lip-lip constant of any Lip-lip space in the sense of Keith [27] is equal to 1, and new nonembeddability results.
ISSN:2299-3274
2299-3274
DOI:10.1515/agms-2016-0005