We solve the Björling 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 and an analytic (timelike in the case of de Sitter three-space) unit vector field N along and orthogonal to γ, there exists a unique (spacelike in the case of de Sitter three-space) surface of constant mean curvature 1 which contains γ and the unit normal of which on γ is N. Some of the consequences are the planar reflection principles, and a classification of rotationally invariant CMC 1 surfaces.
Bibliographical noteFunding Information:
The first author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF-2014R1A2A2A01003683). The second author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2009-0093827).
© 2017 Korean Mathematical Society.
- Björling formula
- Constant mean curvature surfaces
- De sitter space
ASJC Scopus subject areas
- General Mathematics