Volume bounds for the quantitative singular strata of non collapsed RCD metric measure spaces
Metric Geometry
2019-07-08 v1
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 \cite{CheegerNaber13a}. 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 (\cite[Remark 3.8]{DePhilippisGigli18}) of ncRCD(K,N) spaces.
Keywords
Cite
@article{arxiv.1907.02735,
title = {Volume bounds for the quantitative singular strata of non collapsed RCD metric measure spaces},
author = {Gioacchino Antonelli and Elia Bruè and Daniele Semola},
journal= {arXiv preprint arXiv:1907.02735},
year = {2019}
}