Calculus of Variations and Geometric Measure Theory

G. Antonelli - E. Bruè - D. Semola

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


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


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.