Hermite polynomials and helicoidal minimal surfaces
Recently it was proved by \textit{M. Weber, D. Hoffmann} and \textit{M. Wolf} [An embedded genus one helicoid. Preprint 2004, http://arxiv.org/abs/math.DG/0401080] that the famous helicoid with a handle constructed by D. Hoffmann, H. Karcher and F. Wei is embedded. In the present paper the authors construct for each \(g \geq 1\) embedded periodic minimal surfaces such that they are asymptotic to the helicoid, invariant under vertical screw motions and translations by \(\pi\), and the quotients have genus \(g\) and two helicoidal ends. As it is mentioned in the summary these surfaces ``suggest a pathway to the construction of higher genus helicoids''.
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