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
[Espaces « non-collapsed » avec courbure de Ricci minorée]

Guido De Philippis ¹ ; Nicola Gigli ¹

¹ SISSA Via Bonomea 265, 34136 Trieste, Italy

Journal de l’École polytechnique — Mathématiques, Tome 5 (2018), pp. 613-650.

Résumé
Abstract

Nous proposons une définition d’espace « non-collapsed » avec courbure de Ricci minorée et nous généralisons aux espaces RCD le théorème de convergence du volume de Colding et l’estimation de l’écart de dimension de Cheeger-Colding. En particulier, ceci prouve la stabilité des espaces RCD « non-collapsed » par rapport à la convergence de Gromov-Hausdorff « non-collapsed ».

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.

Reçu le : 2017-08-27
Accepté le : 2018-06-10
Publié le : 2018-08-28

MR Zbl

DOI : 10.5802/jep.80

Classification : 53C23, 53C21
Keywords: Ricci curvature bounded from below, non-collapsed spaces
Mots-clés : Courbure de Ricci minorée, espace “non-collapsed”

Affiliations des auteurs :

Guido De Philippis ¹ ; Nicola Gigli ¹

¹ SISSA Via Bonomea 265, 34136 Trieste, Italy

Licence :

CC-BY-ND 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Guido De Philippis and Nicola Gigli},
     title = {Non-collapsed spaces with {Ricci} curvature bounded from below},
     journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
     pages = {613--650},
     publisher = {\'Ecole polytechnique},
     volume = {5},
     year = {2018},
     doi = {10.5802/jep.80},
     zbl = {06988590},
     mrnumber = {3852263},
     language = {en},
     url = {https://jep.centre-mersenne.org/articles/10.5802/jep.80/}
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Guido De Philippis; Nicola Gigli. Non-collapsed spaces with Ricci curvature bounded from below. Journal de l’École polytechnique — Mathématiques, Tome 5 (2018), pp. 613-650. doi : 10.5802/jep.80. https://jep.centre-mersenne.org/articles/10.5802/jep.80/

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