Gradient estimates for the Neumann heat flow on non-convex domains of metric measure spaces

Jeudi 23 mai 15:45-16:45 - Karl Theodor Sturm

Résumé : We briefly recall the Eulerian and the Lagrangian approach to synthetic lower Ricci bounds on metric measure spaces due to Bakry-Emery and Lott-Sturm-Villani, resp., and present recent extensions to spaces with variable lower Ricci bounds. Our main results will be a gradient estimate for the heat flow with Neumann boundary conditions on domains of metric measure spaces obtained through „convexification“ of the domains by means of subtle time changes. This improves upon previous results both in the case of non-convex domains and in the case of convex domains.

Lieu : IMO, salle 3L8

Gradient estimates for the Neumann heat flow on non-convex domains of metric measure spaces  Version PDF