Uniquely minimizing costs for the Kantorovitch problem
Abbas Moameni, Ludovic Rifford · Annales de la faculté des sciences de Toulouse Mathématiques · 2020
The purpose of the present paper is to establish comprehensive and systematic sufficient conditions for uniqueness of the Kantorovitch optimizer, and to prove the density of continuous costs on arbitrary manifolds for which optimal plans are unique. We shall also establish a practical criterion for the uniqueness of the Kantorovitch optimizer in the non-compact setting on Polish spaces.