Non-collapsed spaces with Ricci curvature bounded from below
[Espaces « non-collapsed » avec courbure de Ricci minorée]
Journal de l’École polytechnique — Mathématiques, Tome 5 (2018), pp. 613-650.

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 :
Accepté le :
Publié le :
DOI : 10.5802/jep.80
Classification : 53C23, 53C21
Keywords: Ricci curvature bounded from below, non-collapsed spaces
Mot clés : Courbure de Ricci minorée, espace “non-collapsed”

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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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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