Multi-valued graphs in embedded constant mean curvature disks

Details Multi-valued graphs in embedded constant mean curvature disks Multi-valued graphs in embedded constant mean curvature disks

2004-09-10

arxiv.org/abs/math/0409184v1

Mathematics

Differential Geometry

22 pages, 13 figures

Scientific paper

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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