On the fundamental tone of immersions and submersions

Cavalcante, Marcos; Manfio, Fernando

doi:10.1090/proc/13969

On the fundamental tone of immersions and submersions
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by Marcos P. Cavalcante and Fernando Manfio

Proc. Amer. Math. Soc. 146 (2018), 2963-2971

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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