The ends of a complete embedded minimal surface of {em finite totalcurvature} are well understood (every such end is asymptotic to a catenoid orto 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 ahelicoid. The result applies, in particular, to the genus one helicoid andimplies that it is embedded outside of a compact set in ${mathbb R}^3$.
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