## Hiroshima Mathematical Journal

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

#### 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
Revised: 26 June 2019
First available in Project Euclid: 7 March 2020

https://projecteuclid.org/euclid.hmj/1583550013

Digital Object Identifier
doi:10.32917/hmj/1583550013

Mathematical Reviews number (MathSciNet)
MR4074377

Zentralblatt MATH identifier
07197868

#### 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