On Harnack inequalities and optimal transportation

• Dominique Bakry ^[1] ; Ivan Gentil ^[2] ; Michel Ledoux ^[1]
  1. [1] Université de Toulouse

     Université de Toulouse

     Arrondissement de Toulouse, Francia

     
  2. [2] Claude Bernard University Lyon 1

     Claude Bernard University Lyon 1

     Arrondissement de Lyon, Francia

     
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 14, Nº 3, 2015, págs. 705-727
• Idioma: inglés
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• Resumen

  • We develop connections between Harnack inequalities for the heat flow of diffusion operators with curvature bounded from below and optimal transportation.

    Through heat kernel inequalities, a new isoperimetric-type Harnack inequality is emphasized. Commutation properties between the heat and Hopf- Lax semigroups are developed consequently, providing direct access to heat flow contraction in Wasserstein spaces