Geometriae Dedicata

, 137:143 | Cite as

Distortions of the helicoid

Original Paper

Abstract

Colding and Minicozzi have shown that an embedded minimal disk \({0\in\Sigma\subset B_R}\) in \({\mathbb{R}^3}\) with large curvature at 0 looks like a helicoid on the scale of R. Near 0, this can be sharpened: on the scale of |A|−1(0), Σ is close, in a Lipschitz sense, to a piece of a helicoid. We use surfaces constructed by Colding and Minicozzi to see this description cannot hold on the scale R.

Keywords

Differential geometry Minimal surfaces 

Mathematics Subject Classification (2000)

49Q05 53A10 

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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Massachusetts Institute of TechnologyCambridgeUSA
  2. 2.Johns Hopkins UniversityBaltimoreUSA

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