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The gaussian image of mean curvature one surfaces in hyperbolic space of finite total curvature
Collin, Pascal ; Hauswirth, Laurent ; Rosenberg, Harold
HAL, hal-00796830 / Harvested from HAL
Text on HAL
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.
Publié le : 2002-07-05
Classification:  gauss map,  constant mean curvature one surface,  hyperbolic space,  [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG] 
@article{hal-00796830,
     author = {Collin, Pascal and Hauswirth, Laurent and Rosenberg, Harold},
     title = {The gaussian image of mean curvature one surfaces in hyperbolic space of finite total curvature},
     journal = {HAL},
     volume = {2002},
     number = {0},
     year = {2002},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00796830}
}

Collin, Pascal; Hauswirth, Laurent; Rosenberg, Harold. The gaussian image of mean curvature one surfaces in hyperbolic space of finite total curvature. HAL, Tome 2002 (2002) no. 0, . http://gdmltest.u-ga.fr/item/hal-00796830/