Graphs with constant mean curvature in the 3-hyperbolic space
2002 ◽
Vol 74
(3)
◽
pp. 371-377
◽
Keyword(s):
In this work we will deal with disc type surfaces of constant mean curvature in the three dimensional hyperbolic space which are given as graphs of smooth functions over planar domains. From the various types of graphs that could be defined in the hyperbolic space we consider in particular the horizontal and the geodesic graphs. We proved that if the mean curvature is constant, then such graphs are equivalent in the following sense: suppose that M is a constant mean curvature surface in the 3-hyperbolic space such that M is a geodesic graph of a function rho that is zero at the boundary, then there exist a smooth function f that also vanishes at the boundary, such that M is a horizontal graph of f. Moreover, the reciprocal is also true.
2007 ◽
Vol 11
(4)
◽
pp. 651-670
◽
2016 ◽
Vol 28
(11)
◽
pp. 3691-3702
◽
2005 ◽
Vol 16
(02)
◽
pp. 101-110
◽
2019 ◽
Vol 150
(6)
◽
pp. 3216-3230
2008 ◽
Vol 144
(1)
◽
pp. 186-220
◽
1987 ◽
Vol 36
(1)
◽
pp. 19-24
◽
1995 ◽
Vol 10
(03)
◽
pp. 337-364
◽
2011 ◽
Vol 84
(3)
◽
pp. 362-371