English

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

Differential Geometry 2007-05-23 v2

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).

Keywords

Cite

@article{arxiv.math/0206021,
  title  = {Hyperbolic constant mean curvature one surfaces: Spinor representation and trinoids in hypergeometric functions},
  author = {Alexander I. Bobenko and Tatyana V. Pavlyukevich and Boris A. Springborn},
  journal= {arXiv preprint arXiv:math/0206021},
  year   = {2007}
}

Comments

29 pages, 9 figures. v2: figures of cmc1-surfaces corrected

R2 v1 2026-07-22T16:45:47.777Z