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

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

2008-04-29

arxiv.org/abs/0804.4636v1

Proc. Amer. Math. Soc. 137 (2009), no. 3, 1093--1102.

Mathematics

Differential Geometry

9 pages

Scientific paper

10.1090/S0002-9939-08-09680-9

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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