Delaunay Ends of Constant Mean Curvature Surfaces

Details Delaunay Ends of Constant Mean Curvature Surfaces Delaunay Ends of Constant Mean Curvature Surfaces

2007-01-03

arxiv.org/abs/math/0701082v1

Compositio Math. 144 (2008), 186-220

Mathematics

Differential Geometry

Scientific paper

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 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.

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