The geometry of finite topology surfaces properly embedded in hyperbolic space with constant mean curvature one
Collin, Pascal ; Hauswirth, Laurent ; Rosenberg, Harold
HAL, hal-00796822 / Harvested from HAL
Text on HAL
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).
Publié le : 2001-07-05
Classification:  [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG] 
@article{hal-00796822,
     author = {Collin, Pascal and Hauswirth, Laurent and Rosenberg, Harold},
     title = {The geometry of finite topology surfaces properly embedded in hyperbolic space with constant mean curvature one},
     journal = {HAL},
     volume = {2001},
     number = {0},
     year = {2001},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00796822}
}

Collin, Pascal; Hauswirth, Laurent; Rosenberg, Harold. The geometry of finite topology surfaces properly embedded in hyperbolic space with constant mean curvature one. HAL, Tome 2001 (2001) no. 0, . http://gdmltest.u-ga.fr/item/hal-00796822/