Non-collapsed spaces with Ricci curvature bounded from below

Published 7 Aug 2017 in math.MG | (1708.02060v3)

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 ${\sf RCD}$ spaces. In particular this establishes the stability of non-collapsed spaces under non-collapsed Gromov-Hausdorff convergence.

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