2 citations · 3 across the 19 of their papers we have counts for
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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…