descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 30 Aug 2017Embargo end date: 01 Jan 2016 English Publisher:World Scientific Pub Co Pte LtJournal:Communications in Contemporary Mathematics, volume 19, page 1,750,007 (issn: 0219-1997, eissn: 1793-6683,

Authors: Fabio Cavalletti; Fabio Cavalletti; Andrea Mondino;

doi: 10.1142/s0219199717500079 , 10.48550/arxiv.1609.00782

arXiv: http://arxiv.org/abs/1609.00782

handle: 2434/1011228 , 20.500.11767/44728

Optimal maps in essentially non-branching spaces

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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.

Related Organizations

International School for Advanced Studies
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Keywords

Mathematics - Functional Analysis, Mathematics - Metric Geometry, existence of maps; measure contraction property; Optimal transport; uniqueness of maps, FOS: Mathematics, existence of maps; measure contraction property; Optimal transport; uniqueness of maps;, Metric Geometry (math.MG), QA, Functional Analysis (math.FA)

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