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Journal Article

Spectral estimates and discreteness of spectra under Riemannian submersions

MPS-Authors
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Polymerakis,  Panagiotis
Max Planck Institute for Mathematics, Max Planck Society;

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Fulltext (public)

1910.00860.pdf
(Preprint), 217KB

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Citation

Polymerakis, P. (2020). Spectral estimates and discreteness of spectra under Riemannian submersions. Annals of Global Analysis and Geometry, 57(2), 349-363. doi:10.1007/s10455-020-09703-y.


Cite as: http://hdl.handle.net/21.11116/0000-0005-EE55-0
Abstract
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, for Riemannian submersions of complete manifolds with closed fibers of bounded mean curvature, we show that the spectrum of the base space is discrete if and only if the spectrum of the total space is discrete.