42 citations · 102 across the 21 of their papers we have counts for
23 papers
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…
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 f…
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.
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…
On the Spectrum of Certain Hadamard Manifolds
Werner Ballmann, Mayukh Mukherjee, Panagiotis Polymerakis
We show the absolute continuity of the spectrum and determine the spectrum as a set for two classes of Hadamard manifolds and for specific domains and quotients of one of the class…
Bottom of spectra and coverings of orbifolds
Werner Ballmann, Panagiotis Polymerakis
We discuss the behaviour of the bottom of the spectrum of scalar Schrödinger operators under Riemannian coverings of orbifolds. We apply our results to geometrically finite and to…