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Volume bounds for the quantitative singular strata of non collapsed RCD metric measure spaces

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.
Publication status:
Published
Peer review status:
Peer reviewed

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Publisher:
De Gruyter Open
Journal:
Analysis and Geometry in Metric Spaces More from this journal
Volume:
7
Issue:
1
Pages:
158-178
Publication date:
2019-09-30
Acceptance date:
2019-08-23
DOI:
EISSN:
2299-3274
Language:
English
Keywords:
Pubs id:
1138063
Local pid:
pubs:1138063
Deposit date:
2020-10-20

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