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Embedded Minimal Ends Asymptotic to the Helicoid by McCuan, John; Hoffman, David is a scholarly article available to read on EtoBox.

What is Embedded Minimal Ends Asymptotic to the Helicoid about?

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 ${\mathbb R}^3$.

Author

McCuan, John; Hoffman, David

Published

1997

Language

EN