Multi-valued graphs in embedded constant mean curvature disks

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.

22 pages, 13 figures