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March 2020 Eigenvalue estimates for submanifolds in Hadamard manifolds and product manifolds $N \times \mathbb R$
Jing Mao, Rongqiang Tu, Kai Zeng
Hiroshima Math. J. 50(1): 17-42 (March 2020). DOI: 10.32917/hmj/1583550013

Abstract

In this paper, we investigate submanifolds with locally bounded mean curvature in Hadamard manifolds, product manifolds $N \times \mathbb R$, submanifolds with bounded $\varpi$-mean curvature in the hyperbolic space, and successfully give lower bounds for the weighted fundamental tone and the first eigenvalue of the $p$-Laplacian.

Funding Statement

This work was supported in part by the NSF of China (Grant Nos. 11401131 and 11801496), the Fok Ying-Tung Education Foundation (China), and Key Laboratory of Applied Mathematics of Hubei Province (Hubei University).

Citation

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Jing Mao. Rongqiang Tu. Kai Zeng. "Eigenvalue estimates for submanifolds in Hadamard manifolds and product manifolds $N \times \mathbb R$." Hiroshima Math. J. 50 (1) 17 - 42, March 2020. https://doi.org/10.32917/hmj/1583550013

Information

Received: 4 June 2018; Revised: 26 June 2019; Published: March 2020
First available in Project Euclid: 7 March 2020

zbMATH: 07197868
MathSciNet: MR4074377
Digital Object Identifier: 10.32917/hmj/1583550013

Subjects:
Primary: 53C40
Secondary: 53C42, 58C40

Rights: Copyright © 2020 Hiroshima University, Mathematics Program

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Vol.50 • No. 1 • March 2020
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