2 citations · 3 across the 19 of their papers we have counts for
22 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.
Large Steklov eigenvalues under volume constraints
Alexandre Girouard, Panagiotis Polymerakis
In this note we establish an expression for the Steklov spectrum of warped products in terms of auxiliary Steklov problems for drift Laplacians with weight induced by the warping f…
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…
Normal covering spaces with maximal bottom of spectrum
Panagiotis Polymerakis
We study the property of spectral-tightness of Riemannian manifolds, which means that the bottom of the spectrum of the Laplacian separates the universal covering space from any ot…
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…
Small eigenvalues of Schrödinger operators over geometrically finite manifolds
Werner Ballmann, Panagiotis Polymerakis
We estimate the number of small eigenvalues of Schrödinger operators on Riemannian vector bundles over geometrically finite manifolds.
On the Steklov spectrum of covering spaces and total spaces
Panagiotis Polymerakis
We show the existence of a natural Dirichlet-to-Neumann map on Riemannian manifolds with boundary and bounded geometry, such that the bottom of the Dirichlet spectrum is positive.…
The spectrum of the Laplacian and volume growth of proper minimal submanifolds
G. Pacelli Bessa, Vicent Gimeno, Panagiotis Polymerakis
We give upper bounds for the bottom of the essential spectrum of properly immersed minimal submanifolds of in terms of their volume growth. Our result improves the…
On the essential spectrum of differential operators over geometrically finite orbifolds
Werner Ballmann, Panagiotis Polymerakis
We discuss the essential spectrum of essentially self-adjoint elliptic differential operators of first order and of Laplace type operators on Riemannian vector bundles over geometr…
On the differential form spectrum of geometrically finite orbifolds
Werner Ballmann, Panagiotis Polymerakis
We derive lower bounds for the essential spectrum of the Hodge-Laplacian on geometrically finite orbifolds and their suborbifolds.
Spectral estimates for Riemannian submersions with fibers of basic mean curvature
Panagiotis Polymerakis
For Riemannian submersions with fibers of basic mean curvature, we compare the spectrum of the total space with the spectrum of a Schrödinger operator on the base manifold. Exploit…
Equivariant discretizations of diffusions and harmonic functions of bounded growth
Werner Ballmann, Panagiotis Polymerakis
For covering spaces and properly discontinuous actions with compatible diffusion operators, we discuss Lyons-Sullivan discretizations of the associated diffusions and harmonic func…
Bottom of spectra and coverings
Werner Ballmann, Panagiotis Polymerakis
We discuss the behaviour of the bottom of the spectrum of scalar Schrödinger operators under Riemannian coverings.
Spectral estimates and discreteness of spectra under Riemannian submersions
Panagiotis Polymerakis
For Riemannian submersions, we establish some estimates for the spectrum of the total space in terms of the spectrum of the base space and the geometry of the fibers. In particular…
Positive harmonic functions on groups and covering spaces
Panagiotis Polymerakis
We show that if is a normal Riemannian covering, with closed, and has exponential volume growth, then there are non-constant, positive harmonic functions…
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…
Coverings preserving the bottom of the spectrum
Panagiotis Polymerakis
We prove that if a Riemannian covering preserves the bottom of the spectrum of a Schrödinger operator, which belongs to the discrete spectrum of the operator on the base manifold,…
Bottom of spectra and amenability of coverings
Werner Ballmann, Henrik Matthiesen, Panagiotis Polymerakis
For a Riemannian covering , the bottoms of the spectra of and coincide if the covering is amenable. The converse implication does not always hold. A…
On the spectrum of differential operators under Riemannian coverings
Panagiotis Polymerakis
For a Riemannian covering , we compare the spectrum of an essentially self-adjoint differential operator on a bundle with the sp…
On the bottom of spectra under coverings
Werner Ballmann, Henrik Matthiesen, Panagiotis Polymerakis
For a Riemannian covering of complete Riemannian manifolds with boundary (possibly empty) and respective fundamental groups , we show that the bottoms…