On surfaces with constant mean curvature in hyperbolic space
de Lima, Ronaldo F.
Illinois J. Math., Tome 47 (2003) no. 4, p. 1079-1098 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
It is shown that for a complete surface with constant mean curvature $H>1$ in $\mathbb{H}\kern0.5pt ^3$ with boundary and finite index the distance function to the boundary is bounded. We apply this result to establish a sharp height estimate for certain geodesic graphs with noncompact boundary. We also show that a geodesically complete, embedded surface in $\mathbb{H}\kern0.5pt ^3$ with constant mean curvature $H>1$ and bounded Gaussian curvature is proper and has an $\epsilon -$tubular neighborhood on its mean convex side that is embedded. Finally, we use this last result to obtain a monotonicity formula for such a surface.
Publié le : 2003-10-15
Classification:  53A10,  53A35 
@article{1258138092,
     author = {de Lima, Ronaldo F.},
     title = {On surfaces with constant mean curvature in hyperbolic space},
     journal = {Illinois J. Math.},
     volume = {47},
     number = {4},
     year = {2003},
     pages = { 1079-1098},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258138092}
}

de Lima, Ronaldo F. On surfaces with constant mean curvature in hyperbolic space. Illinois J. Math., Tome 47 (2003) no. 4, pp.  1079-1098. http://gdmltest.u-ga.fr/item/1258138092/