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BY 4.0 license Open Access Published by De Gruyter Open Access September 30, 2019

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

Gioacchino Antonelli EMAIL logo , Elia Brué and Daniele Semola

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.

MSC 2010: 53C23; 28A75; 53C21

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Received: 2019-07-05
Accepted: 2019-08-23
Published Online: 2019-09-30

© 2019 Gioacchino Antonelli et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution 4.0 Public License.

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