Existence and uniqueness of optimal maps on Alexandrov spaces

• Autores: Jérôme Bertrand
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 219, Nº 3, 2008, págs. 838-851
• Idioma: inglés
• DOI: 10.1016/j.aim.2008.06.008
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• Resumen

  • The purpose of this paper is to show that in a finite dimensional metric space with Alexandrov's curvature bounded below, Monge's transport problem for the quadratic cost admits a unique solution.