English

Meromorphic Potentials and Smooth CMC Surfaces

dg-ga 2008-02-03 v2 Differential Geometry

Abstract

This work is based on the approach developed by J.~Dorfmeister, F.~Pedit and H.~Wu [GANG and KITCS preprint, Report KITCS94-4-1] to construct maps Φ:DR3\Phi:D\rightarrow R^3, DD being the unit disk in CC, whose images are surfaces of constant mean curvature. They start from certain meromorphic one forms, so called meromorphic potentials, which take values in a twisted loop algebra over su(2)su(2). The authors give necessary and sufficient conditions on the meromorphic potential for the constructed map Φ\Phi to be an immersion. This revision corrects several misprints and minor TeX problems.

Keywords

Cite

@article{arxiv.dg-ga/9412007,
  title  = {Meromorphic Potentials and Smooth CMC Surfaces},
  author = {J. Dorfmeister and G. Haak},
  journal= {arXiv preprint arXiv:dg-ga/9412007},
  year   = {2008}
}

Comments

39 pages, LaTeX2e format, LaTeX 2.09 optional, 2 postscript figures not included, they can be obtained via WWW. point your WWW client at: http://poincare.math.ukans.edu/CMC.html This is a revision correcting several misprints and TeX problems