On the geometry of constant mean curvature one surfaces in hyperbolic space
Sa Earp, Ricardo ; Toubiana, Eric
Illinois J. Math., Tome 45 (2001) no. 4, p. 371-401 / Harvested from Project Euclid
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We give a geometric classification of regular ends with constant mean curvature $1$ and finite total curvature, embedded in hyperbolic space. We prove that each such end is either asymptotic to a catenoid cousin or asymptotic to a horosphere. We also study symmetry properties of constant mean curvature $1$ surfaces in hyperbolic space associated to minimal surfaces in Euclidean space. We describe the constant mean curvature $1$ surfaces in $\hi3$ associated to the family of surfaces in $\m3$ that is isometric to the helicoid.
Publié le : 2001-04-15
Classification:  53C42,  53A10 
@article{1258138346,
     author = {Sa Earp, Ricardo and Toubiana, Eric},
     title = {On the geometry of constant mean curvature one surfaces in hyperbolic space},
     journal = {Illinois J. Math.},
     volume = {45},
     number = {4},
     year = {2001},
     pages = { 371-401},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258138346}
}

Sa Earp, Ricardo; Toubiana, Eric. On the geometry of constant mean curvature one surfaces in hyperbolic space. Illinois J. Math., Tome 45 (2001) no. 4, pp.  371-401. http://gdmltest.u-ga.fr/item/1258138346/