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  Spectral estimates for Riemannian submersions with fibers of basic mean curvature

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.

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Polymerakis_Spectral estimates for Riemannian submersions with fibers of basic mean curvature_2021.pdf (Publisher version), 379KB
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Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
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2003.09843.pdf (Preprint), 319KB
 
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https://doi.org/10.1007/s12220-021-00634-z (Publisher version)
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 Creators:
Polymerakis, Panagiotis1, Author           
Affiliations:
1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Differential Geometry, Spectral Theory
 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.

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Language(s): eng - English
 Dates: 2021
 Publication Status: Issued
 Pages: -
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 Table of Contents: -
 Rev. Type: Peer
 Identifiers: arXiv: 2003.09843
DOI: 10.1007/s12220-021-00634-z
 Degree: -

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Title: Journal of Geometric Analysis
  Abbreviation : J. Geom. Anal.
Source Genre: Journal
 Creator(s):
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Publ. Info: Springer
Pages: - Volume / Issue: 31 (10) Sequence Number: - Start / End Page: 9951 - 9980 Identifier: -