Hermite polynomials and helicoidal minimal surfaces
type: Item
instance of: scholarly article
title: Hermite polynomials and helicoidal minimal surfaces
zbMATH Open document ID: 1075.53010
author: Martin Traizet
author: Matthias Weber
published in: Inventiones Mathematicae
publication date: 2005-08-02T00:00:00Z
review text: 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''.
Mathematics Subject Classification ID: 53A10
Mathematics Subject Classification ID: 49Q05
zbMATH DE Number: 2190621
zbMATH Keywords: minimal surfaces
zbMATH Keywords: helicoids
reviewed by: I. A. Taimanov
MaRDI profile type: Publication
full work available at URL: s00222-004-0420-1
OpenAlex ID: W2068242590
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DOI: 10.1007/S00222-004-0420-1
description: scientific article