Optimal transport maps on Alexandrov spaces revisited
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
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Manuscripta MathematicaDate
2022Discipline
Analyysin ja dynamiikan tutkimuksen huippuyksikköMatematiikkaAnalysis and Dynamics Research (Centre of Excellence)MathematicsCopyright
© 2021 the Authors
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.
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Springer Science and Business Media LLCISSN Search the Publication Forum
0025-2611Publication in research information system
https://converis.jyu.fi/converis/portal/detail/Publication/100240117
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Open access funding provided by University of Jyväskylä (JYU).License
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