Eigenvalue estimates for submanifolds with locally bounded mean curvature in 𝑁×ℝ

Bessa, G.; Costa, M.

doi:10.1090/S0002-9939-08-09680-9

Eigenvalue estimates for submanifolds with locally bounded mean curvature in $N \times \mathbb {R}$
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by G. Pacelli Bessa and M. Silvana Costa PDF

Proc. Amer. Math. Soc. 137 (2009), 1093-1102 Request permission

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 have a positive fundamental tone.

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