Non-collapsed spaces with Ricci curvature bounded from below

Guido De Philippis; Nicola Gigli

Non-collapsed spaces with Ricci curvature bounded from below

Metric Geometry 2025-06-24 v3

Authors: Guido De Philippis , Nicola Gigli

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.

Keywords

ricci curvature and riemannian geometry topological spaces general topology

Cite

@article{arxiv.1708.02060,
  title  = {Non-collapsed spaces with Ricci curvature bounded from below},
  author = {Guido De Philippis and Nicola Gigli},
  journal= {arXiv preprint arXiv:1708.02060},
  year   = {2025}
}

Comments

Clarified the proof of Proposition 3.2, in particular step 2.2 (thank to Liming Yin for pointing this out)

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