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Optimal transport maps on Alexandrov spaces revisited

Tapio RajalaTimo Schultz

subject

Mathematics - Differential GeometryClass (set theory)Pure mathematicsGeneral MathematicsExistential quantificationPlan (drawing)Algebraic geometryoptimaalisuusCurvatureMeasure (mathematics)Primary 53C23. Secondary 49K30Mathematics - Analysis of PDEsMathematics - Metric GeometryFOS: Mathematicsmass transportationMathematics::Metric GeometryMathematicsAlexandrov-avaruudetMetric Geometry (math.MG)Number theoryDifferential Geometry (math.DG)Bounded functionMathematics::Differential GeometrymassasiirtoAlexandrov spacesAnalysis of PDEs (math.AP)

description

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.

yearjournalcountryeditionlanguage
2018-03-27
http://arxiv.org/abs/1803.10023