Kim, Young-Heon; McCann, Robert J.; Warren, Micah Pseudo-Riemann geometry calibrates optimal transportation. (English) Zbl 1222.49059 Math. Res. Lett. 17, No. 6, 1183-1197 (2010). Summary: Given a transportation cost \(c:M\times\overline{M}\rightarrow\mathbb R\), optimal maps minimize the total cost of moving masses from \(M\) to \(\overline{M}\). We find, explicitly, a pseudo-metric and a calibration form on \(M\times\overline{M}\) such that the graph of an optimal map is a calibrated maximal submanifold, and hence has zero mean curvature. We define the mass of space-like currents in spaces with indefinite metrics. Cited in 19 Documents MSC: 49Q20 Variational problems in a geometric measure-theoretic setting 53B21 Methods of local Riemannian geometry Keywords:pseudo-Riemann geometry; optimal transportation; maximal submanifold; zero mean curvature PDFBibTeX XMLCite \textit{Y.-H. Kim} et al., Math. Res. Lett. 17, No. 6, 1183--1197 (2010; Zbl 1222.49059) Full Text: DOI arXiv