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Article Dans Une Revue Annals of Mathematics Année : 2001

The geometry of finite topology surfaces properly embedded in hyperbolic space with constant mean curvature one

Résumé

We prove that in the three dimensional hyperbolic space H(3) the properly embedded constant mean curvature one surfaces with finite topology are of finite total curvature and each ends are regular. This imply in particular that the hrosphere is the only properly embedded simply connected constant mean curvature one surface in H(3).
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Dates et versions

hal-00796822 , version 1 (05-03-2013)

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  • HAL Id : hal-00796822 , version 1

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Pascal Collin, Laurent Hauswirth, Harold Rosenberg. The geometry of finite topology surfaces properly embedded in hyperbolic space with constant mean curvature one. Annals of Mathematics, 2001, 153, pp.623-659. ⟨hal-00796822⟩
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