Non-collapsed spaces with Ricci curvature bounded from below

Guido De Philippis; Nicola Gigli

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Non-collapsed spaces with Ricci curvature bounded from below

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arxiv 1708.02060 v3 pith:BULRZ6DV submitted 2017-08-07 math.MG

Guido De Philippis , Nicola Gigli This is my paper

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keywords non-collapsedspacesbelowboundedconvergencecurvaturericcicheeger-colding

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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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