Inventiones mathematicae

, Volume 161, Issue 1, pp 113–149

Hermite polynomials and helicoidal minimal surfaces

Article

DOI: 10.1007/s00222-004-0420-1

Cite this article as:
Traizet, M. & Weber, M. Invent. math. (2005) 161: 113. doi:10.1007/s00222-004-0420-1

Abstract

The main objective of this paper is to construct smooth 1-parameter families of embedded minimal surfaces in euclidean space that are invariant under a screw motion and are asymptotic to the helicoid. Some of these families are significant because they generalize the screw motion invariant helicoid with handles and thus suggest a pathway to the construction of higher genus helicoids. As a byproduct, we are able to relate limits of minimal surface families to the zero-sets of Hermite polynomials.

Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques et Physique Théorique, Faculté des Sciences et TechniquesUniversité François RabelaisToursFrance
  2. 2.Department of MathematicsIndiana UniversityBloomingtonUSA

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