Existence of vertical ends of mean curvature 1/2 in ℍ²×ℝ

Elbert, Maria; Nelli, Barbara; Sa Earp, Ricardo

doi:10.1090/S0002-9947-2011-05361-4

Existence of vertical ends of mean curvature $1/2$ in $\mathbb {H}^2 \times \mathbb {R}$
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by Maria Fernanda Elbert, Barbara Nelli and Ricardo Sa Earp

Trans. Amer. Math. Soc. 364 (2012), 1179-1191

DOI: https://doi.org/10.1090/S0002-9947-2011-05361-4

Published electronically: November 7, 2011

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Abstract:

We prove the existence of graphs over exterior domains of $\mathbb {H}^2\times \{0\},$ of constant mean curvature $H=\frac {1}{2}$ in $\mathbb {H}^2\times \mathbb {R}$ and weak growth equal to the embedded rotational examples.

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Existence of vertical ends of mean curvature $1/2$ in $\mathbb {H}^2 \times \mathbb {R}$
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Abstract: