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arXiv · 1007.1549

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

Pierre Bérard·Philippe Castillon·Marcos P. Cavalcante
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Abstract

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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Pierre Bérard, Philippe Castillon, Marcos P. Cavalcante. 2010-07-09. Eigenvalue estimates for hypersurfaces in $H^m \times R$ and applications. https://arxiv.org/abs/1007.1549

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