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Multi-valued graphs in embedded constant mean curvature disks

Giuseppe Tinaglia
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Abstract

In this paper we prove that an embedded and simply connected constant mean curvature surface with curvature large at a point contains a multi-valued graph around that point on the scale of $|A|^2$, where $|A|^2$ is the norm squared of the second fundamental form. This generalizes Colding and Minicozzi's result for minimal surfaces.

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Giuseppe Tinaglia. 2004-09-10. Multi-valued graphs in embedded constant mean curvature disks. https://arxiv.org/abs/math/0409184

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