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Distortions of the Helicoid

Authors
  • Bernstein, Jacob
  • Breiner, Christine
Type
Published Article
Publication Date
May 30, 2008
Submission Date
May 30, 2008
Source
arXiv
License
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External links

Abstract

Colding and Minicozzi have shown that an embedded minimal disk $0\in\Sigma\subset B_R$ in $\Real^3$ with large curvature at 0 looks like a helicoid on the scale of $R$. Near 0, this can be sharpened: on the scale of $|A|^{-1}(0)$, $\Sigma$ 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 $R$.

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