Annals of Global Analysis and Geometry

, Volume 12, Issue 1, pp 341–355 | Cite as

On helicoidal ends of minimal surfaces

  • Pascal Romon
Article
Received:

Abstract

This article analyzes the behaviour of helicoidal ends of properly embedded minimal surfaces, namely properly embedded infinite total curvature minimal annuli of parabolic type, satisfying a growth condition on the curvature via the Gauss map, and a geometric transversality condition. Then we show that embeddedness forces the end to be asymptotic either to a plane, or a helicoid or a spiraling helicoid. In all three cases, the Gauss map can be described in very simple terms. Finally this local result yields a global corollary stating the rigidity of embedded minimal helicoids.

Key words

Minimal surface infinite total curvature annular end helicoid embeddedness essential singularity 

MSC 1991

53 A 10 
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Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • Pascal Romon
    • 1
  1. 1.Centre de Mathématiques et Leurs Applications Unité de Recherche Associée CNRS 1611École Normale Supérieure de CachanCachan CedexFrance

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