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On complete mean curvature 1/2 surfaces in H(2) x R

Abstract : For a complete embedded surface with compact boundary and constant mean curvature 1/2 in H(2) x R lying on one side of a horocylinder, we prove an analogue of the Hoffman-Meeks half-space theorem. As an application, we show that a complete immersed surface of constant mean curvature 1/2 which is transverse to the vertical killing field must be an entire graph. Moreover, to each holomorphic quadratic differential on the unit disk or C we can associate an entire graph of constant mean curvature 1/2.
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https://hal-upec-upem.archives-ouvertes.fr/hal-00693562
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Submitted on : Wednesday, May 2, 2012 - 6:14:51 PM
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  • HAL Id : hal-00693562, version 1

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Laurent Hauswirth, Harold Rosenberg, Joel Spruck. On complete mean curvature 1/2 surfaces in H(2) x R. Communications in Analysis and Geometry, 2008, 16 (5), pp.989--1005. ⟨hal-00693562⟩

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