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
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
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