On the bottom of spectra under coverings

Werner Ballmann; Henrik Matthiesen; Panagiotis Polymerakis

On the bottom of spectra under coverings

Differential Geometry 2019-09-09 v2 Spectral Theory

Authors: Werner Ballmann , Henrik Matthiesen , Panagiotis Polymerakis

Abstract

For a Riemannian covering $M_1\to M_0$ of complete Riemannian manifolds with boundary (possibly empty) and respective fundamental groups $\Gamma_1\subseteq\Gamma_0$ , we show that the bottoms of the spectra of $M_0$ and $M_1$ coincide if the right action of $\Gamma_0$ on $\Gamma_1\backslash\Gamma_0$ is amenable.

Keywords

riemannian covering bottom of spectrum complete riemannian manifold fundamental group amenable group right action

Cite

@article{arxiv.1701.02130,
  title  = {On the bottom of spectra under coverings},
  author = {Werner Ballmann and Henrik Matthiesen and Panagiotis Polymerakis},
  journal= {arXiv preprint arXiv:1701.02130},
  year   = {2019}
}

Comments

8 pages, fixed a technical mistake concerning the volume of the boundary of fundamental domains

On the bottom of spectra under coverings

Abstract

Keywords

Cite

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