Volume Bounds for the Quantitative Singular Strata of Non Collapsed RCD Metric Measure Spaces

Abstract

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 [13]. 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 ([20, Remark 3.8]) of ncRCD(K, N) spaces.