Horizontal diffusion in C^1 path space
2009-03-11 14:30 2009-03-11 15:30 2009-03-11 14:30 .. 15:30
by Marc Arnaudon (Univ. Poitiers)
We define horizontal diffusions in C1 path space over a Riemannian manifold and prove their existence. In case the metric on the manifold is solution to the forward Ricci flow, horizontal diffusion along Brownian motion is length preserving. As application, we prove non-increasing properties in the Monge-Kantorovich minimization problem for two probability measures evoluting along the heat flow.