Embedded minimal ends asymptotic to the helicoid

Details Embedded minimal ends asymptotic to the helicoid Embedded minimal ends asymptotic to the helicoid

1997-10-09

arxiv.org/abs/math/9710207v1

Mathematics

Differential Geometry

Scientific paper

The ends of a complete embedded minimal surface of {\em finite total curvature} are well understood (every such end is asymptotic to a catenoid or to a plane). We give a similar characterization for a large class of ends of {\em infinite total curvature}, showing that each such end is asymptotic to a helicoid. The result applies, in particular, to the genus one helicoid and implies that it is embedded outside of a compact set in ${\mathbb R}^3$.

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