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