Non-collapsed spaces with Ricci curvature bounded from below

By Guido De Philippis, Nicola Gigli. 2017

159 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/f8c1aa539f8da1df5ad6440a44a9656c2eed2e55

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In Applied Mathematics

1. Enrico Pasqualetto
2. Elia Brué
3. Semola Daniele

In Astronomy and Astrophysics

1. Enrico Pasqualetto
2. Elia Brué
3. Semola Daniele

In Geometry and Topology

1. Semola Daniele
2. Elia Brué
3. Enrico Pasqualetto

Citations in the corpus

• Rectifiability of the reduced boundary for sets of finite perimeter over $\RCD(K,N)$ spaces. (2019, background): “When specialized to the non-collapsed case (see [44]), where the only non-empty regular set is the top dimensional one, Theorem 4.”