6 papers · 1 filter
Small eigenvalues of pseudo-Laplacians
Werner Ballmann, Sugata Mondal, Panagiotis Polymerakis
We extend the Otal-Rosas bound on the number of small eigenvalues of the Laplacian on a hyperbolic surface to the small eigenvalues of pseudo-Laplacians. In the process, we extend…
Equivariant discretizations of diffusions, random walks, and harmonic functions
Werner Ballmann, Panagiotis Polymerakis
For covering spaces and properly discontinuous actions with compatible diffusion processes, we discuss Lyons-Sullivan discretizations of the processes and the associated function t…
Martin boundaries of diffusions and random walks on hyperbolic spaces
Werner Ballmann, Debanjan Nandi, Panagiotis Polymerakis
We discuss certain kinds of diffusions on hyperbolic spaces, associated random walks on discrete groups of isometries of the latter, and their Martin boundaries.
On the spectral stability of finite coverings
Werner Ballmann, Sugata Mondal, Panagiotis Polymerakis
We prove the non-existence of new eigenvalues in for specific and random finite coverings of a complete and connected Riemannian manifold with Ricci curvature bounded…
Guide to Boundary Value Problems for Dirac-Type Operators
Christian Baer, Werner Ballmann
We present an introduction to boundary value problems for Dirac-type operators on complete Riemannian manifolds with compact boundary. We introduce a very general class of boundary…
Spectral instability of coverings
Sugata Mondal, Werner Ballmann
We study the behaviour of eigenvalues, below the bottom of the essential spectrum, of the Laplacian under finite Riemannian coverings of complete and connected Riemannian manifolds…