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arXiv · 1803.07353

Bottom of spectra and amenability of coverings

Werner Ballmann·Henrik Matthiesen·Panagiotis Polymerakis
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Abstract

For a Riemannian covering $\pi\colon M_1\to M_0$, the bottoms of the spectra of $M_0$ and $M_1$ coincide if the covering is amenable. The converse implication does not always hold. Assuming completeness and a lower bound on the Ricci curvature, we obtain a converse under a natural condition on the spectrum of $M_0$.

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Werner Ballmann, Henrik Matthiesen, Panagiotis Polymerakis. 2018-03-20. Bottom of spectra and amenability of coverings. https://arxiv.org/abs/1803.07353

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