Half-space theorems for mean curvature one surfaces in hyperbolic space

Rodriguez, Lucio; Rosenberg, Harold

doi:10.1090/S0002-9939-98-04510-9

Half-space theorems for mean curvature one surfaces in hyperbolic space
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by Lucio Rodriguez and Harold Rosenberg PDF

Proc. Amer. Math. Soc. 126 (1998), 2755-2762 Request permission

Abstract:

We give conditions which oblige properly embedded constant mean curvature one surfaces in hyperbolic 3-space to intersect. Our results are inspired by the theorem that two disjoint properly immersed minimal surfaces in $\mathbf {R}^3$ must be planes.

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