Embedded minimal ends asymptotic to the helicoid
Abstract
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 ${\mathbb R}^3$.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 October 1997
 DOI:
 10.48550/arXiv.math/9710207
 arXiv:
 arXiv:math/9710207
 Bibcode:
 1997math.....10207M
 Keywords:

 Mathematics  Differential Geometry