# Vertical Ends of Constant Mean Curvature H=1-2 in H^2 imes R

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We prove a vertical halfspace theorem for surfaces with constant mean curvature $H={1-2},$ properly immersed in the product space $\h^2\times e,$ where $\h^2$ is the hyperbolic plane and $e$ 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 $\h^2\times e.$

Autor: Barbara Nelli; Ricardo Sa Earp

Fuente: https://archive.org/