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 spaces. In particular this establishes the stability of non-collapsed spaces under non-collapsed Gromov-Hausdorff convergence.
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@article{JEP_2018__5__613_0,
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/}
}
TY - JOUR AU - Guido De Philippis AU - Nicola Gigli TI - Non-collapsed spaces with Ricci curvature bounded from below JO - Journal de l’École polytechnique — Mathématiques PY - 2018 SP - 613 EP - 650 VL - 5 PB - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.80/ DO - 10.5802/jep.80 LA - en ID - JEP_2018__5__613_0 ER -
%0 Journal Article %A Guido De Philippis %A Nicola Gigli %T Non-collapsed spaces with Ricci curvature bounded from below %J Journal de l’École polytechnique — Mathématiques %D 2018 %P 613-650 %V 5 %I École polytechnique %U https://jep.centre-mersenne.org/articles/10.5802/jep.80/ %R 10.5802/jep.80 %G en %F JEP_2018__5__613_0
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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