Eigenvalue estimates for hypersurfaces in $H^m \times R$ and applications

Details Eigenvalue estimates for hypersurfaces in $H^m \times R$ and applications Eigenvalue estimates for hypersurfaces in $H^m \times R$ and applications

2010-07-09

arxiv.org/abs/1007.1549v1

Mathematics

Differential Geometry

Scientific paper

In this paper, we give a lower bound for the spectrum of the Laplacian on minimal hypersurfaces immersed into $H^m \times R$. As an application, in dimension 2, we prove that a complete minimal surface with finite total extrinsic curvature has finite index. On the other hand, for stable, minimal surfaces in $H^3$ or in $H^2 \times \R$, we give an upper bound on the infimum of the spectrum of the Laplacian and on the volume growth.

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