Existence and structure of solutions of Steiner problems in optimal transport.

摘要

We study the Steiner problem of finding a minimal spanning network in the setting of a space of probability measures with metric defined by cost of optimal transport between measures. Existence of a solution is shown for the Wasserstein space Pp( X ) over any base space X which is a separable, locally compact Hadamard space. Structural results are given for the case p = 2 under further restrictions on X .