Minimal hypersurfaces in $\HH^n \times \R$, total curvature and index

Details Minimal hypersurfaces in $\HH^n \times \R$, total curvature and index Minimal hypersurfaces in $\HH^n \times \R$, total curvature and index

2008-08-28

arxiv.org/abs/0808.3838v3

Mathematics

Differential Geometry

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Scientific paper

In this paper, we consider minimal hypersurfaces in the product space $\mathbb{H}^n \times \mathbb{R}$. We begin by studying examples of rotation hypersurfaces and hypersurfaces invariant under hyperbolic translations. We then consider minimal hypersurfaces with finite total curvature. This assumption implies that the corresponding curvature goes to zero uniformly at infinity. We show that surfaces with finite total intrinsic curvature have finite index. The converse statement is not true as shown by our examples which also serve as useful barriers.

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