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

created by bruè on 05 Jul 2019

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Submitted Paper

Inserted: 5 jul 2019
Last Updated: 5 jul 2019

Year: 2019

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.