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arXiv · 1402.6886

Constructions of $H_r$-hypersurfaces, barriers and Alexandrov Theorem in $H^n \times R$

Maria Fernanda Elbert·Ricardo Sa Earp
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Abstract

In this paper, we are concerned with hypersurfaces in $H^n\times R$ with constant r-mean curvature, to be called $H_r$-hypersurfaces. We construct examples of complete $H_r$-hypersurfaces which are invariant by parabolic screw motion or by rotation. We prove that there is a unique rotational strictly convex entire $H_r$-graph for each value $0 \frac{n-r}{n}$, there is a unique embedded compact strictly convex rotational $H_r$-hypersurface. By using them as barriers, we obtain some interesting geometric results, including height estimates and an Alexandrov-type Theorem. Namely, we prove that an embedded compact $H_r$-hypersurface in $H^n\times R$ is rotational ($H_r>0$).

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Maria Fernanda Elbert, Ricardo Sa Earp. 2014-02-27. Constructions of $H_r$-hypersurfaces, barriers and Alexandrov Theorem in $H^n \times R$. https://arxiv.org/abs/1402.6886

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