Vertical Ends of Constant Mean Curvature H=1/2 in H^2\times R

Details Vertical Ends of Constant Mean Curvature H=1/2 in H^2\times R Vertical Ends of Constant Mean Curvature H=1/2 in H^2\times R

2008-03-14

arxiv.org/abs/0803.2244v2

Mathematics

Differential Geometry

This is a revised version of the article that we submit before. There was a problem in the construction of graphical ends. We

Scientific paper

We prove a vertical halfspace theorem for surfaces with constant mean curvature $H={1/2},$ properly immersed in the product space $\h^2\times\re,$ where $\h^2$ is the hyperbolic plane and $\re$ is the set of real numbers. The proof is a geometric application of the classical maximum principle for second order elliptic PDE, using the family of non compact rotational $H=1/2$ surfaces in $\h^2\times\re.$

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