Distortions of the Helicoid

Details Distortions of the Helicoid Distortions of the Helicoid

2008-05-30

arxiv.org/abs/0805.4775v1

Mathematics

Differential Geometry

4 pages, 3 figures

Scientific paper

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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