Abstract
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.
Reference17 articles.
1. Surfaces of Mean Curvature One in Hyperbolic Space;BRYANT R.;Astérisque,1987
2. A rigidity theorem for properly embedded minimal surfaces in R3;CHOI HI;J Diff Geom,1990
3. The geometry of finite topology Bryant surfaces;COLLIN P;Ann of Math,2001
4. Complete minimal surfaces in R3 of genus one and four planar embedded ends;COSTA CJ;Proc of Amer Math Soc,1993
5. The topology of complete minimal surfaces of finite total Gaussian curvature;JORGE L;Topology,,1983
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