Online Talk 

Zoom link: https://princeton.zoom.us/j/594605776

It is a joint work with I. Mondello (Paris XII) and D. Tewodrose (UL Bruxelles, Nantes). A Kato bound on the Ricci curvature yields nice geometric properties ( eigenvalue lower bound, heat kernel estimates...); in particular it implies a doubling condition for the Riemannian volume and hence a precompactness result in the Gromov-Hausdorff topology. We have obtained results that are generalization of the ones of Cheeger and Colding (where a uniform lower bound on the Ricci curvature is assumed).