Event № 803
The Bonnet-Myers theorem states that a complete manifold with Ricci curvature bounded below by a positive threshold is compact with an explicit diameter bound and that its fundamental group is finite. The talk will consist of a review of several extensions of this result. In particular, we will explain how assumptions on the Schrödinger operator with Ricci curvature as potential imply finiteness of the fundamental group of a compact manifold. Those are implied by the so-called Kato condition on the negative part of Ricci curvature. We will also give a purely geometric condition that suffices for the Ricci curvature to be Kato.