On Harnack inequalities and optimal transportation
  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 the heat flow contraction property along Wasserstein distances. 
Dominique Bakry (IUF, IMT), Ivan Gentil (ICJ), Michel Ledoux (IUF,   IMT)
math.PR