A1 Journal article (refereed)
Optimal transport maps on Alexandrov spaces revisited (2022)

Rajala, T., & Schultz, T. (2022). Optimal transport maps on Alexandrov spaces revisited. Manuscripta Mathematica, 169(1-2), 1-18. https://doi.org/10.1007/s00229-021-01333-3

JYU authors or editors

Publication details

All authors or editorsRajala, Tapio; Schultz, Timo

Journal or seriesManuscripta Mathematica



Publication year2022

Publication date20/08/2021


Issue number1-2

Pages range1-18

PublisherSpringer Science and Business Media LLC

Publication countryGermany

Publication languageEnglish


Publication open accessOpenly available

Publication channel open accessPartially open access channel

Publication is parallel published (JYX)https://jyx.jyu.fi/handle/123456789/77448

Publication is parallel publishedhttps://arxiv.org/abs/1803.10023


We 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)-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.


Free keywordsAlexandrov spaces; mass transportation

Contributing organizations

Ministry reportingYes

Reporting Year2022

JUFO rating1

Last updated on 2024-30-04 at 18:15