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arXiv · 0804.4636

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

G. Pacelli Bessa·M. Silvana Costa
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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 $K_{N} \leq \kappa$. When the immersion is minimal our estimates are sharp. We also show that cylindrically bounded minimal surfaces has positive fundamental tone.

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G. Pacelli Bessa, M. Silvana Costa. 2008-04-29. Eigenvalue Estimates for submanifolds of $N \times \mathbb{R}$ with locally bounded mean curvature. https://doi.org/10.1090/s0002-9939-08-09680-9

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