Spectral estimates for Riemannian submersions with fibers of basic mean 
curvature

Polymerakis, Panagiotis

doi:10.1007/s12220-021-00634-z

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Spectral estimates for Riemannian submersions with fibers of basic mean curvature

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Polymerakis, Panagiotis
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1007/s12220-021-00634-z
(Publisher version)

https://doi.org/10.48550/arXiv.2003.09843
(Preprint)

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Polymerakis_Spectral estimates for Riemannian submersions with fibers of basic mean curvature_2021.pdf
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Citation

Polymerakis, P. (2021). Spectral estimates for Riemannian submersions with fibers of basic mean curvature. Journal of Geometric Analysis, 31(10), 9951-9980. doi:10.1007/s12220-021-00634-z.

Cite as: https://hdl.handle.net/21.11116/0000-0008-67BE-F

Abstract

For Riemannian submersions with fibers of basic mean curvature, we compare
the spectrum of the total space with the spectrum of a Schr\"{o}dinger operator
on the base manifold. Exploiting this concept, we study submersions arising
from actions of Lie groups. In this context, we extend the state of the art
results on the bottom of the spectrum under Riemannian coverings. As an
application, we compute the bottom of the spectrum and the Cheeger constant of
connected, amenable Lie groups.