Non-collapsed spaces with Ricci curvature bounded from below

Guido De Philippis; Nicola Gigli

doi:10.5802/jep.80

Non-collapsed spaces with Ricci curvature bounded from below

Guido De Philippis, Nicola Gigli

Mathematics

Research output: Contribution to journal › Article › peer-review

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

Original language	English (US)
Pages (from-to)	613-650
Number of pages	38
Journal	Journal de l'Ecole Polytechnique - Mathematiques
Volume	5
DOIs	https://doi.org/10.5802/jep.80
State	Published - 2018

ASJC Scopus subject areas

General Mathematics

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abstract = "— We propose a definition of non-collapsed space with Ricci curvature bounded from below and we prove the versions of Colding{\textquoteright}s volume convergence theorem and of Cheeger-Colding dimension gap estimate for RCD spaces. In particular this establishes the stability of non-collapsed spaces under non-collapsed Gromov-Hausdorff convergence.",

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Non-collapsed spaces with Ricci curvature bounded from below

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