Infinitesimal Structure of Differentiability Spaces, and Metric Differentiation

• Main Authors: Cheeger Jeff, Kleiner Bruce, Schioppa Andrea
• Format: Article
• Language: English
• Published: De Gruyter 2016-08-01
• Series: Analysis and Geometry in Metric Spaces
• Subjects: metric measure space; bi-lipschitz embedding; measurable differentiable structure; differentiability space; metric differentiation
• Online Access: https://doi.org/10.1515/agms-2016-0005
• ISSN: 2299-3274

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.