EMBEDDED MINIMAL ENDS ASYMPTOTIC TO THE HELICOID

JOHN MCCUAN AND DAVID HOFFMAN

Abstract. The ends of a complete embedded minimal surface of 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 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 ℝ^{3}.