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Article Dans Une Revue Advanced Studies in Pure Mathematics Année : 2002

The gaussian image of mean curvature one surfaces in hyperbolic space of finite total curvature

Résumé

The hyperbolic Gauss map G of a complete constant mean curvature one surface M in hyperbolic 3-space, is a holomorphic map from M to the Riemann sphere. When M has finite total curvature, we prove G can miss at most three points unless G is constant. We also prove that if M is a properly embedded mean curvature one surface of finite topology, then G is surjective unless M is a horosphere or catenoid cousin.
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Dates et versions

hal-00796830 , version 1 (05-03-2013)

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  • HAL Id : hal-00796830 , version 1

Citer

Pascal Collin, Laurent Hauswirth, Harold Rosenberg. The gaussian image of mean curvature one surfaces in hyperbolic space of finite total curvature. Advanced Studies in Pure Mathematics, 2002, 34, pp.9-14. ⟨hal-00796830⟩
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