Optimal transport maps on Alexandrov spaces revisited
Abstract
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.
Main Authors
Format
Articles
Research article
Published
2022
Series
Subjects
Publication in research information system
Publisher
Springer Science and Business Media LLC
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202108234613Käytä tätä linkitykseen.
Review status
Peer reviewed
ISSN
0025-2611
DOI
https://doi.org/10.1007/s00229-021-01333-3
Language
English
Published in
Manuscripta Mathematica
Citation
- 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
License
Additional information about funding
Open access funding provided by University of Jyväskylä (JYU).
Copyright© 2021 the Authors