In [5], the genus one helicoid was constructed and strong evidence was given that it is embedded. The surface has infinite total curvature and contains two orthogonal, intersecting straight lines. Its single end has Weierstrass data modeled on that of the helicoid. It is conformally a punctured disk, on which both dh and dg/g have double poles at the puncture. Moreover, these forms have no residues. (See the next section for details about the Weierstrass representation and the helicoid.) In this paper we study this type of end. Our main result is the following.
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