37 citations · 202 across the 38 of their papers we have counts for
4 papers · 1 filter
Universal lower bounds for Laplacians on weighted graphs
Daniel Lenz, Peter Stollmann
We discuss optimal lower bounds for eigenvalues of Laplacians on weighted graphs. These bounds are formulated in terms of the geometry and, more specifically, the inradius of subse…
Bounds on the first Betti number - an approach via Schatten norm estimates on semigroup differences
Marcel Hansmann, Christian Rose, Peter Stollmann
We derive new estimates for the first Betti number of compact Riemannian manifolds. Our approach relies on the Birman-Schwinger principle and Schatten norm estimates for semigroup…
Manifolds with Ricci curvature in the Kato class: heat kernel bounds and applications
Christian Rose, Peter Stollmann
We review recent results about heat kernel estimates based on Kato conditions on the negative part of the Ricci curvature.
The Kato class on compact manifolds with integral bounds on the negative part of Ricci curvature
Christian Rose, Peter Stollmann
We show that under Ricci curvature integral assumptions the dimension of the first cohomology group can be estimated in terms of the Kato constant of the negative part of the Ricci…