Eigenvalue Estimates for submanifolds of N × R with locally bounded mean curvature

الأصل · EN

We give lower bounds for the fundamental tone of open sets in submanifolds with locally bounded mean curvature in N × R, where N is an n-dimensional complete Riemannian manifold with radial sectional curvature Kₙ ≤ κ. When the immersion is minimal our estimates are sharp. We also show that cylindrically bounded minimal surfaces has positive fundamental tone.