A representation formula for the Laplacian of the distance function

In the seminar I will present a recent work in collaboration with Fabio Cavalletti (SISSA) where, using techniques from optimal transportation, we prove a rather explicit representation formula for the Laplacian of the distance function in spaces with Ricci curvature bounded below. Even if the paper deals with rather general non-smooth spaces, since some results seem new even for smooth manifolds, the seminar will be mostly focused on the smooth framework.



This seminar is organized within the PRIN 2015 Research project «Variational methods, with applications to problems in mathematical physics and geometry» Grant Registration 2015KB9WPT_010, funded by MIUR – Project coordinator Prof. Gianmaria Verzini