Recent developments for Kato type Ricci curvature conditions

Differential Geometry Seminar: Abstract: The Kato condition is a tool from perturbation theory of Dirichlet forms to control perturbed heat semigroups. Using this as a more general condition than Lp-bounds for the negative part of Ricci curvature, I will discuss several recent results in part obtained with Gilles Carron from Nantes, such as Lichnerowicz and isoperimetric constant estimates for compact manifolds as well as a very recent generalization of Myers’ compactness theorem.