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Publication 1

On the Constructability of a Negatively Curved Complete Constant Mean Curvature Surface in the Hyperbolic Space Determined by a Prescribed Hopf Differential.
The Journal of Geometric Analysis, Volume 13, Number 3, 2003, 35 pages, pp 521-555.

Abstract: The constructability of a negatively curved complete constant mean curvature surface in the hyperbolic 3-space based on a prescribed quadratic differential is studied. The explicit structure of the coefficient function of a Hopf differential which guarantees the existence of a unique embedding of a unit disk into the hyperbolic 3-space in such a manner that the embedded surface becomes a complete constant mean curvature surface is provided.

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