Optimal transport maps on Alexandrov spaces revisited
classification
🧮 math.MG
math.APmath.DG
keywords
optimalalexandrovplanspacestransportalternativebelowbounded
read the original 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.
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