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On the fundamental tone of immersions and submersions


Authors: Marcos P. Cavalcante and Fernando Manfio
Journal: Proc. Amer. Math. Soc. 146 (2018), 2963-2971
MSC (2010): Primary 35P15, 53C20
DOI: https://doi.org/10.1090/proc/13969
Published electronically: February 8, 2018
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Abstract: In this paper we obtain lower bound estimates of the spectrum of the Laplace-Beltrami operator on complete submanifolds with bounded mean curvature, whose ambient space admits a Riemannian submersion over a Riemannian manifold with negative sectional curvature. Our main theorem generalizes many previously known estimates and applies for both immersions and submersions.


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Additional Information

Marcos P. Cavalcante
Affiliation: Instituto de Matemática, Universidade Federal de Alagoas, Maceió, AL, CEP 57072-970, Brazil
Email: marcos@pos.mat.ufal.br

Fernando Manfio
Affiliation: ICMC, Universidade de São Paulo, São Carlos, SP, CEP 13561-060, Brazil
Email: manfio@icmc.usp.br

DOI: https://doi.org/10.1090/proc/13969
Keywords: Eigenvalues, Mean Curvature, Isometric immersions, Riemannian submersions
Received by editor(s): May 15, 2017
Received by editor(s) in revised form: September 18, 2017
Published electronically: February 8, 2018
Communicated by: Guofang Wei
Article copyright: © Copyright 2018 American Mathematical Society

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