6 papers
Integral Ricci curvature and the mass gap of Dirichlet Laplacians on domains
Xavier Ramos Olivé, Christian Rose, Lili Wang +1
We obtain a fundamental gap estimate for classes of bounded domains with quantitative control on the boundary in a complete manifold with integral bounds on the negative part of th…
Quantitative Sobolev extensions and the Neumann heat kernel for integral Ricci curvature conditions
Olaf Post, Xavier Ramos Olivé, Christian Rose
We prove the existence of Sobolev extension operators for certain uniform classes of domains in a Riemannian manifold with an explicit uniform bound on the norm depending only on t…
Spectrally positive Bakry-Émery Ricci curvature on graphs
Florentin Münch, Christian Rose
We investigate analytic and geometric implications of non-constant Ricci curvature bounds. We prove a Lichnerowicz eigenvalue estimate and finiteness of the fundamental group assum…
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…
Geometric and spectral estimates based on spectral Ricci curvature assumptions
Gilles Carron, Christian Rose
We obtain a Bonnet-Myers theorem under a spectral condition: a closed Riemannian manifold for which the lowest eigenvalue of the Ricci tensor is such that the Schrödi…
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.