Halfspace theorems for mean curvature one surfaces in hyperbolic space
Authors:
Lucio Rodriguez and Harold Rosenberg
Journal:
Proc. Amer. Math. Soc. 126 (1998), 27552762
MSC (1991):
Primary 53A10
MathSciNet review:
1458259
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Abstract 
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Abstract: We give conditions which oblige properly embedded constant mean curvature one surfaces in hyperbolic 3space to intersect. Our results are inspired by the theorem that two disjoint properly immersed minimal surfaces in must be planes.
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 [AR]
 H. Alencar and H. Rosenberg, Some remarks on the existence of hypersurfaces of constant mean curvature with a given boundary, or asymptotic boundary, in hyperbolic space, Bull. des Sciences Maths. de France 121 (1997), 6169.
 [B]
 B. Bryant, Surfaces of mean curvature one in hyperbolic space, Astérisque 154155 (1987), 341347.
 [C]
 P. Castillon, Sur le surfaces de révolution à courbure moyenne constante dans l'espace hyperbolique, Preprint.
 [doCL]
 M. do Carmo and B. Lawson, On AlexanderBernstein theorems in hyperbolic space, Duke Math. J. 50 (1983), 9951003. MR 85f:53009
 [HM]
 D. Hoffman and W. Meeks, The strong halfspace theorem for minimal surfaces, Invent. Math. 101 (1990), 373377. MR 92e:53010
 [LR]
 G. Levitt and H. Rosenberg, Symmetries of constant mean curvature hypersurfaces in hyperbolic space, Duke Math. J. 52 (1985), 5359. MR 86h:53063
 [S]
 A. Silveira, Stability of complete noncompact surfaces with constant mean curvature, Math. Ann. 277 (1987), 629638.
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Additional Information
Lucio Rodriguez
Affiliation:
Institute for PureApplied Mathematics, Estrada Dona Castorina 110, 22460 Rio de Janeiro, Brazil
Email:
lucio@impa.br
Harold Rosenberg
Affiliation:
Department of Mathematics, University of Paris VII, 2 place Jussieu, 75251 Paris, France
Email:
rosen@math.jussieu.fr
DOI:
http://dx.doi.org/10.1090/S0002993998045109
PII:
S 00029939(98)045109
Received by editor(s):
September 10, 1996
Communicated by:
Peter Li
Article copyright:
© Copyright 1998
American Mathematical Society
