# Infinitesimal Structure of Differentiability Spaces, and Metric Differentiation

Jeff Cheeger; Bruce Kleiner; Andrea Schioppa

Analysis and Geometry in Metric Spaces (2016)

- Volume: 4, Issue: 1, page 104-159, electronic only
- ISSN: 2299-3274

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topJeff Cheeger, Bruce Kleiner, and Andrea Schioppa. "Infinitesimal Structure of Differentiability Spaces, and Metric Differentiation." Analysis and Geometry in Metric Spaces 4.1 (2016): 104-159, electronic only. <http://eudml.org/doc/286768>.

@article{JeffCheeger2016,

abstract = {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.},

author = {Jeff Cheeger, Bruce Kleiner, Andrea Schioppa},

journal = {Analysis and Geometry in Metric Spaces},

keywords = {Metric measure space; bi-Lipschitz embedding; measurable differentiable structure; differentiability
space; metric differentiation; metric measure space; differentiability space},

language = {eng},

number = {1},

pages = {104-159, electronic only},

title = {Infinitesimal Structure of Differentiability Spaces, and Metric Differentiation},

url = {http://eudml.org/doc/286768},

volume = {4},

year = {2016},

}

TY - JOUR

AU - Jeff Cheeger

AU - Bruce Kleiner

AU - Andrea Schioppa

TI - Infinitesimal Structure of Differentiability Spaces, and Metric Differentiation

JO - Analysis and Geometry in Metric Spaces

PY - 2016

VL - 4

IS - 1

SP - 104

EP - 159, electronic only

AB - 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.

LA - eng

KW - Metric measure space; bi-Lipschitz embedding; measurable differentiable structure; differentiability
space; metric differentiation; metric measure space; differentiability space

UR - http://eudml.org/doc/286768

ER -

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