Optimal transport maps on Alexandrov spaces revisited-Reference-Cited by-同舟云学术

Optimal transport maps on Alexandrov spaces revisited

Published:2021-08-20 Issue: Volume: Page:
ISSN:0025-2611
Container-title:manuscripta mathematica
language:en
Short-container-title:manuscripta math.

Author:

Rajala Tapio^ORCID,Schultz Timo

Abstract

AbstractWe give an alternative proof for the fact that in n-dimensional Alexandrov spaces with curvature bounded below there exists a unique optimal transport plan from any purely

$$(n-1)$$

( n - 1 ) -unrectifiable starting measure, and that this plan is induced by an optimal map. Our proof does not rely on the full optimality of a given plan but rather on the c-monotonicity, thus we obtain the existence of transport maps for wider class of (possibly non-optimal) transport plans.

Funder

Luonnontieteiden ja Tekniikan Tutkimuksen Toimikunta

Publisher

Springer Science and Business Media LLC

Subject

General Mathematics

Link

https://link.springer.com/content/pdf/10.1007/s00229-021-01333-3.pdf

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