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Multi-valued graphs in embedded constant mean curvature disks

Research paper by Giuseppe Tinaglia

Indexed on: 10 Sep '04Published on: 10 Sep '04Published in: Mathematics - Differential Geometry



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.