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http://dx.doi.org/10.4134/BKMS.b150984

BJÖRLING FORMULA FOR MEAN CURVATURE ONE SURFACES IN HYPERBOLIC THREE-SPACE AND IN DE SITTER THREE-SPACE  

Yang, Seong-Deog (Department of Mathematics Korea University)
Publication Information
Bulletin of the Korean Mathematical Society / v.54, no.1, 2017 , pp. 159-175 More about this Journal
Abstract
We solve the $Bj{\ddot{o}}rling$ problem for constant mean curvature one surfaces in hyperbolic three-space and in de Sitter three-space. That is, we show that for any regular, analytic (and spacelike in the case of de Sitter three-space) curve ${\gamma}$ and an analytic (timelike in the case of de Sitter three-space) unit vector field N along and orthogonal to ${\gamma}$, there exists a unique (spacelike in the case of de Sitter three-space) surface of constant mean curvature 1 which contains ${\gamma}$ and the unit normal of which on ${\gamma}$ is N. Some of the consequences are the planar reflection principles, and a classification of rotationally invariant CMC 1 surfaces.
Keywords
$Bj{\ddot{o}}rling$ formula; constant mean curvature surfaces; de Sitter space;
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