Ilaria Mondello

Gromov-Hausdorff limits of manifolds with a Kato bound on the Ricci curvature

The goal of this talk is to present some recent results on manifolds for which the negative part of the Ricci curvature satisfies a Kato bound, inspired by Kato potentials in the Euclidean space. This condition is implied for instance by a lower Ricci curvature bound, or an integral Ricci bound in the spirit of Gallot and Petersen-Wei. We will explain some analytic consequences of a Kato bound, and how we used them to study the structure of Gromov-Hausdorff limits of manifolds satisfying this kind of bounds. This talk is based on a joint work with G. Carron and D. Tewodrose.