Calculus of Variations and Geometric Measure Theory

G. De Philippis - N. Gigli

Non-collapsed spaces with Ricci curvature bounded from below

created by dephilipp on 07 Aug 2017
modified on 18 Dec 2019



Inserted: 7 aug 2017
Last Updated: 18 dec 2019

Year: 2017

ArXiv: 1708.02060 PDF


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.