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Delaunay Ends of Constant Mean Curvature Surfaces

M. Kilian·W. Rossman·N. Schmitt
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Abstract

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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M. Kilian, W. Rossman, N. Schmitt. 2007-01-03. Delaunay Ends of Constant Mean Curvature Surfaces. https://doi.org/10.1112/s0010437x07003119

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