Christian Rose (Technische Universität Chemnitz)
We show that if the negative part of the Ricci curvature of a compact manifold is in the Kato-class, the Cheeger constant of the manifold can be bounded below by a positive constant. This is obtained by suitable heat kernel and eigenvalue estimates as well as a Buser-type inequality which relates the Cheeger constant and the first non-zero eigenvalue.
