Resumen de On Harnack inequalities and optimal transportation

Dominique Bakry, Ivan Gentil, Michel Ledoux

• 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