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Delaunay ends of constant mean curvature surfaces

Part of: Classical differential geometry

Published online by Cambridge University Press:  01 January 2008

M. Kilian ,
W. Rossman  and
N. Schmitt
M. Kilian
Affiliation:
Institut für Mathematik, Universität Mannheim, 68131 Mannheim, Germany (email: kilian@rumms.uni-mannheim.de)
W. Rossman
Affiliation:
Department of Mathematics, Kobe University, Rokko Kobe 657-8501, Japan (email: wayne@math.kobe-u.ac.jp)
N. Schmitt
Affiliation:
Mathematisches Institut, Universität Tübingen, 72076 Tübingen, Germany (email: nick@gang.umass.edu, nschmitt@mathmatik.uni-tuebingen.de)
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Abstract

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The generalized Weierstrass representation is used to analyze the asymptotic behavior of a constant mean curvature surface that arises locally from an ordinary differential equation (ODE) with a regular singularity. We prove that a holomorphic perturbation of an ODE that represents a Delaunay surface generates a constant mean curvature surface which has a properly immersed end that is asymptotically Delaunay. Furthermore, that end is embedded if the Delaunay surface is unduloidal.

Keywords

constant mean curvature surfaceasymptoticsDelaunay surfacegeneralized Weierstrass representation

MSC classification

Secondary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature
Type
Research Article
Information
Compositio Mathematica , Volume 144 , Issue 1 , January 2008 , pp. 186 - 220
Copyright
Copyright © Foundation Compositio Mathematica 2008

References

The first and second authors were partially supported by EPSRC Grant GR/S28655/01 and JSPS Grant Kiban-B 15340023, respectively.