Pseudo-Riemannian geometry calibrates optimal transportation

2009/07/28 by Young‐Heon Kim, Young-Heon Kim, Kim, Young-Heon +4 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities #math.AP #math.DG #msc:35J60 #msc:49Q15

paper · pdf · doi:10.48550/arxiv.0907.4962

14 Pages. More thorough proofs and different exposition from the last version. The name is slightly changed.

arxiv created 2010/04/12 · arxiv updated 2010/04/13

Abstract

Given a transportation cost c: M × M \toR, optimal maps minimize the total cost of moving masses from M to M. We find a pseudo-metric and a calibration form on M× M such that the graph of an optimal map is a calibrated maximal submanifold. We define the mass of space-like currents in spaces with indefinite metrics.

Citations

• The geometry of optimal transportation
• Calibrated geometries

Cited by

• Boundary regularity of optimal transport maps on convex domains

Related

• The geometry of optimal transportation
• Mass Transportation on Sub-Riemannian Manifolds
• Metric conditions that guarantee existence and uniqueness of Optimal Transport maps
• Limit Theorems for Optimal Mass Transportation
• An inverse problem in optimal transport on closed Riemannian manifolds