Hyperbolic constant mean curvature one surfaces: Spinor representation and trinoids in hypergeometric functions

2002/06/14 by Alexander I. Bobenko, Tatyana V. Pavlyukevich, Boris A. Springborn · 1 citation
Computer Science · Mathematics · #Algebraic and Geometric Analysis #Geometric and Algebraic Topology #Polynomial and algebraic computation #math.DG #msc:53A10 #msc:53C42

paper · pdf · doi:10.1007/s00209-003-0511-5

published as Math. Z. 245, 63--91(2003) · 29 pages, 9 figures. v2: figures of cmc1-surfaces corrected

arxiv created 2002/06/14 · openalex publication_date 2003/09/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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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• Dressing preserving the fundamental group

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