Optimal transport maps on Alexandrov spaces revisited

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...

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Veröffentlicht in:	Manuscripta mathematica 2022-09, Vol.169 (1-2), p.1-18
Hauptverfasser:	Rajala, Tapio, Schultz, Timo
Format:	Artikel
Sprache:	eng
Schlagworte:	Algebraic Geometry Calculus of Variations and Optimal Control Optimization Geometry Lie Groups Mathematics Mathematics and Statistics Number Theory Optimization Topological Groups Transportation planning
Online-Zugang:	Volltext
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