# Volume bounds for the quantitative singular strata of non collapsed RCD metric measure spaces

created by bruè on 05 Jul 2019
modified by semola on 30 May 2020

[BibTeX]

Published Paper

Inserted: 5 jul 2019
Last Updated: 30 may 2020

Journal: Anal. Geom. Metr. Spaces
Volume: 7
Number: 1
Pages: 158--178
Year: 2019
Doi: https://doi.org/10.1515/agms-2019-0008

Abstract:

The aim of this note is to generalize to the class of non collapsed $\RCD(K,N)$ metric measure spaces the volume bound for the effective singular strata obtained by Cheeger and Naber for non collapsed Ricci limits in CN13. The proof, which is based on a quantitative differentiation argument, closely follows the original one. As a simple outcome we provide a volume estimate for the enlargement of Gigli-DePhilippis' boundary (DePG18, Remark 3.8) of $\ncRCD(K,N)$ spaces.