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Article Dans Une Revue Communications in Analysis and Geometry Année : 2008

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

Résumé

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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Dates et versions

hal-00693562 , version 1 (02-05-2012)

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  • HAL Id : hal-00693562 , version 1

Citer

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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