Hiroshima Mathematical Journal

Eigenvalue estimates for submanifolds in Hadamard manifolds and product manifolds $N \times \mathbb R$

Jing Mao, Rongqiang Tu, and Kai Zeng

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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.

Note

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).

Article information

Source
Hiroshima Math. J., Volume 50, Number 1 (2020), 17-42.

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

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1583550013

Digital Object Identifier
doi:10.32917/hmj/1583550013

Mathematical Reviews number (MathSciNet)
MR4074377

Zentralblatt MATH identifier
07197868

Subjects
Primary: 53C40: Global submanifolds [See also 53B25]
Secondary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42] 58C40: Spectral theory; eigenvalue problems [See also 47J10, 58E07]

Keywords
eigenvalues drifting Laplacian $p$-Laplacian Hadamard manifolds product manifolds

Citation

Mao, Jing; Tu, Rongqiang; Zeng, Kai. Eigenvalue estimates for submanifolds in Hadamard manifolds and product manifolds $N \times \mathbb R$. Hiroshima Math. J. 50 (2020), no. 1, 17--42. doi:10.32917/hmj/1583550013. https://projecteuclid.org/euclid.hmj/1583550013


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