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

The aim of this note is to generalize to the class of non collapsed RCD( , ) 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 fo...

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Bibliographic Details
Published in:Analysis and Geometry in Metric Spaces 2019-01, Vol.7 (1), p.158-178
Main Authors: Antonelli, Gioacchino, Brué, Elia, Semola, Daniele
Format: Article
Language:English
Subjects:
28A75
53C21
53C23
Curvature-dimension condition
Enlargement
Non collapsed
Ricci limit space
Singular strata
Strata
Volume bounds
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Summary:The aim of this note is to generalize to the class of non collapsed RCD( , ) 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( , ) spaces.
ISSN:2299-3274
2299-3274
DOI:10.1515/agms-2019-0008