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Quantitative Obata's theorem

Abstract:
We prove a quantitative version of Obata’s Theorem involving the shape of functions with null mean value when compared with the cosine of distance functions from single points. The deficit between the diameters of the manifold and of the corresponding sphere is bounded likewise. These results are obtained in the general framework of (possibly non-smooth) metric measure spaces with curvature-dimension conditions through a quantitative analysis of the transport-rays decompositions obtained by the localization method.
Publication status:
Accepted
Peer review status:
Peer reviewed

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
St Hilda's College
Role:
Author
ORCID:
0000-0002-1932-7148
Publisher:
Mathematical Sciences Publishers Publisher's website
Journal:
Analysis & PDE Journal website
Acceptance date:
2022-01-31
EISSN:
1948-206X
ISSN:
2157-5045
Source identifiers:
1070572
Language:
English
Keywords:
Pubs id:
pubs:1070572
UUID:
uuid:0f420814-dd4a-4546-91d7-0a8268d54cd7
Local pid:
pubs:1070572
Deposit date:
2019-11-20

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