Minimal surfaces in euclidean 3-space and their mean curvature 1 cousins in hyperbolic 3-space
2003 ◽
Vol 75
(3)
◽
pp. 271-278
Keyword(s):
We show that the Hopf differentials of a pair of isometric cousin surfaces, a minimal surface in euclidean 3-space and a constant mean curvature (CMC) one surface in the 3-dimensional hyperbolic space, with properly embedded annular ends, extend holomorphically to each end. Using this result, we derive conditions for when the pair must be a plane and a horosphere.
Keyword(s):
2015 ◽
Vol 26
(02)
◽
pp. 1550014
◽
2011 ◽
Vol 61
(10)
◽
pp. 1845-1853
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2008 ◽
Vol 34
(1)
◽
pp. 73-95
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1995 ◽
Vol 347
(8)
◽
pp. 3177
2013 ◽
Vol 33
(3)
◽
pp. 830-838
◽