Slopes of Kantorovich potentials and existence of optimal transport maps in metric measure spaces View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2014-02

AUTHORS

Luigi Ambrosio, Tapio Rajala

ABSTRACT

We study optimal transportation with the quadratic cost function in geodesic metric spaces satisfying suitable non-branching assumptions. We introduce and study the notions of slope along curves and along geodesics, and we apply the latter to prove suitable generalizations of Brenier’s theorem of existence of optimal maps.

PAGES

71-87

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s10231-012-0266-x

DOI

http://dx.doi.org/10.1007/s10231-012-0266-x

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1009238432


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