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Rectifiability of RCD(K,N) spaces via δ-splitting maps

Abstract:
In this note we give simplified proofs of rectifiability of RCD(K,N) spaces as metric measure spaces and lower semicontinuity of the essential dimension, via δ-splitting maps. The arguments are inspired by the Cheeger-Colding theory for Ricci limits and rely on the second order differential calculus developed by Gigli and on the convergence and stability results by Ambrosio-Honda.
Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.5186/aasfm.2021.4627

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Publisher:
Suomalainen Tiedeakatemia (Finnish Academy of Science and Letters)
Journal:
Annales Fennici Mathematici More from this journal
Volume:
46
Issue:
1
Pages:
465–482
Publication date:
2021-06-21
Acceptance date:
2020-05-27
DOI:
ISSN:
1239-629X
Language:
English
Keywords:
Pubs id:
1140292
Local pid:
pubs:1140292
Deposit date:
2020-11-03

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