Calculus of Variations and Geometric Measure Theory
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G. De Philippis - N. Gigli

Non-collapsed spaces with Ricci curvature bounded from below

created by dephilipp on 07 Aug 2017

[BibTeX]

Preprint

Inserted: 7 aug 2017
Last Updated: 7 aug 2017

Year: 2017

Abstract:

We propose a definition of non-collapsed space with Ricci curvature bounded from below and we prove the versions of Colding's volume convergence theorem and of Cheeger-Colding dimension gap estimate for ${\sf RCD}$ spaces.

In particular this establishes the stability of non-collapsed spaces under non-collapsed Gromov-Hausdorff convergence.


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