Hyperbolic constant mean curvature one surfaces: Spinor representation and trinoids in hypergeometric functions
Alexander I. Bobenko, Tatyana V. Pavlyukevich, Boris A. Springborn
Abstract
We present a global representation for surfaces in 3-dimensional hyperbolic space with constant mean curvature 1 (CMC-1 surfaces) in terms of holomorphic spinors. This is a modification of Bryant's representation. It is used to derive explicit formulas in hypergeometric functions for CMC-1 surfaces of genus 0 with three regular ends which are asymptotic to catenoid cousins (CMC-1 trinoids).
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