Existence and Structure of Solutions of Steiner Problems in Optimal Transport
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چکیده
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 . Readers: Chikako Mese (Advisor) and Joel Spruck.
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