A proof of Sudakov theorem with strictly convex norms

作者：Caravenna Laura^*

来源：Mathematische Zeitschrift, 2011, 268(1-2): 371-407.

DOI：10.1007/s00209-010-0677-6

The paper establishes a solution to the Monge problem in R(n) for a possibly asymmetric norm cost function and absolutely continuous initial measures, under the assumption that the unit ball is strictly convex-but not necessarily differentiable nor uniformly convex. The proof follows the strategy initially proposed by Sudakov in 1976, found to be incomplete in 2000; the missing step is fixed in the above case adapting a disintegration technique introduced for a variational problem. By strict convexity, mass moves along rays, and we also investigate the divergence of the vector field of rays.

• 出版日期2011-6