Meromorphic Potentials and Smooth CMC Surfaces

Details Meromorphic Potentials and Smooth CMC Surfaces Meromorphic Potentials and Smooth CMC Surfaces

1994-12-31

arxiv.org/abs/dg-ga/9412007v2

Mathematics

Differential Geometry

39 pages, LaTeX2e format, LaTeX 2.09 optional, 2 postscript figures not included, they can be obtained via WWW. point your WWW

Scientific paper

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 $\Phi:D\rightarrow R^3$, $D$ being the unit disk in $C$, 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 $su(2)$. The authors give necessary and sufficient conditions on the meromorphic potential for the constructed map $\Phi$ to be an immersion. This revision corrects several misprints and minor TeX problems.

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