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• On deterministic solutions for multi-marginal optimal transport with Coulomb cost 

  Bindini, Ugo; De Pascale, Luigi; Kausamo, Anna (American Institute of Mathematical Sciences (AIMS), 2022)

  In this paper we study the three-marginal optimal mass transportation problem for the Coulomb cost on the plane R2. The key question is the optimality of the so-called Seidl map, first disproved by Colombo and Stra. We ...

• Multi-marginal entropy-transport with repulsive cost 

  Gerolin, Augusto; Kausamo, Anna; Rajala, Tapio (Springer, 2020)

  In this paper we study theoretical properties of the entropy-transport functional with repulsive cost functions. We provide sufficient conditions for the existence of a minimizer in a class of metric spaces and prove the ...

• Existence of optimal transport maps in very strict CD(K,∞) -spaces 

  Schultz, Timo (Springer Berlin Heidelberg, 2018)

  We introduce a more restrictive version of the strict CD(K,∞) -condition, the so-called very strict CD(K,∞) -condition, and show the existence of optimal maps in very strict CD(K,∞) -spaces despite the possible ...

• Slopes of Kantorovich potentials and existence of optimal transport maps in metric measure spaces 

  Ambrosio, Luigi; Rajala, Tapio (Springer, 2014)

  We study optimal transportation with the quadratic cost function in geodesic metric spaces satisfying suitable non-branching assumptions. We introduce and study the notions of slope along curves and along geodesics and we ...

• Tensorization of p-weak differentiable structures 

  Eriksson-Bique, Sylvester; Rajala, Tapio; Soultanis, Elefterios (Elsevier, 2024)

  We consider p-weak differentiable structures that were recently introduced in [9], and prove that the product of p-weak charts is a p-weak chart. This implies that the product of two spaces with a p-weak differentiable ...