Eigenvalue Estimates for submanifolds of $N\times \mathbb{R}$ with locally bounded mean curvature

Abstract

We give lower bounds for the fundamental tone of open sets in submanifolds with locally bounded mean curvature in $N\times \mathbb{R}$, where $N$ is an $n$-dimensional complete Riemannian manifold with radial sectional curvature $K_N\le \kappa$. When the immersion is minimal our estimates are sharp. We also show that cylindrically bounded minimal surfaces has positive fundamental tone.

9 pages

Cited by in corpus (2)

• On submanifolds with tamed second fundamental form
• Eigenvalue estimates for submanifolds of warped product spaces