Title:
Gromov-Hausdorff limits of manifolds with a Kato bound on the Ricci curvature
Abstract: In this talk I will present some recent results
obtained in collaboration with G. Carron and D. Tewodrose about the
structure of Gromov-Hausdorff limits of manifolds with Ricci curvature
satisfying a Kato integral bound. This condition is implied for
instance by a lower Ricci curvature bound, or an integral Ricci bound
in the spirit of the work of Petersen-Wei. After explaining our
setting, we focus on the introduction of new almost monotone
quantities based on the heat kernel, and their role in proving a
regularity theory that recovers previous results by Cheeger and
Colding.