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Optimal maps in essentially non-branching spaces

Abstract:
In this paper we prove that in a metric measure space [Formula: see text] verifying the measure contraction property with parameters [Formula: see text] and [Formula: see text], any optimal transference plan between two marginal measures is induced by an optimal map, provided the first marginal is absolutely continuous with respect to [Formula: see text] and the space itself is essentially non-branching. In particular this shows that there exists a unique transport plan and it is induced by a map.
Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1142/s0219199717500079

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Oxford college:
St Hilda's College
Role:
Author
ORCID:
0000-0002-1932-7148
Publisher:
World Scientific Publishing Publisher's website
Journal:
Communications in Contemporary Mathematics Journal website
Volume:
19
Issue:
6
Article number:
1750007
Publication date:
2017-02-09
Acceptance date:
2016-10-17
DOI:
EISSN:
1793-6683
ISSN:
0219-1997
Source identifiers:
1061593
Language:
English
Keywords:
Pubs id:
pubs:1061593
UUID:
uuid:35e3ec4a-1de2-4114-aea7-20d19b1beee2
Local pid:
pubs:1061593
Deposit date:
2019-10-11

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