Abstract
For a Riemannian covering π : M1 → M0, the bottoms of the spectra of M0 and M1 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 M0.
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Ballmann, W., Matthiesen, H., Polymerakis, P. (2020). Bottom of Spectra and Amenability of Coverings. In: Chen, J., Lu, P., Lu, Z., Zhang, Z. (eds) Geometric Analysis. Progress in Mathematics, vol 333. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-34953-0_2
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DOI: https://doi.org/10.1007/978-3-030-34953-0_2
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-030-34952-3
Online ISBN: 978-3-030-34953-0
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