论文信息 - Monge's transport problem on a Riemannian manifold

Monge's transport problem on a Riemannian manifold

Monge's problem refers to the classical problem of optimally transporting mass: given Borel probability measures μ + ¬= μ - , find the measurepreserving map s: M → M between them which minimizes the average distance transported. Set on a complete, connected, Riemannian manifold M - and assuming absolute continuity of μ + - an optimal map will be shown to exist. Aspects of its uniqueness are also established.

R. McCann | M. Feldman

[1] I. Holopainen. Riemannian Geometry , 1927, Nature.

[2] W. D. Evans,et al. PARTIAL DIFFERENTIAL EQUATIONS , 1941 .

[3] H. Fédérer. Geometric Measure Theory , 1969 .

[4] M. Spivak. A comprehensive introduction to differential geometry , 1979 .

[5] V. Sudakov,et al. Geometric Problems in the Theory of Infinite-dimensional Probability Distributions , 1979 .

[6] L. Evans. Measure theory and fine properties of functions , 1992 .

[7] J. Eschenburg. Comparison Theorems in Riemannian Geometry , 1994 .

[8] M. Feldman. Variational Evolution Problems and Nonlocal Geometric Motion , 1997, math/9710206.

[9] S. Rachev,et al. Mass transportation problems , 1998 .

[10] L. Evans,et al. Differential equations methods for the Monge-Kantorovich mass transfer problem , 1999 .

[11] R. McCann,et al. Constructing optimal maps for Monge's transport problem as a limit of strictly convex costs , 2001 .

[12] N. Trudinger,et al. On the Monge mass transfer problem , 2001 .

[13] R. McCann. Polar factorization of maps on Riemannian manifolds , 2001 .

[14] R. McCann,et al. Uniqueness and transport density in Monge's mass transportation problem , 2002 .