Eigenvalue estimates for hypersurfaces in $H^m \times R$ and applications
Differential Geometry
2019-10-07 v1
Abstract
In this paper, we give a lower bound for the spectrum of the Laplacian on minimal hypersurfaces immersed into . 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 or in , we give an upper bound on the infimum of the spectrum of the Laplacian and on the volume growth.
Keywords
Cite
@article{arxiv.1007.1549,
title = {Eigenvalue estimates for hypersurfaces in $H^m \times R$ and applications},
author = {Pierre Bérard and Philippe Castillon and Marcos P. Cavalcante},
journal= {arXiv preprint arXiv:1007.1549},
year = {2019}
}