In this thesis, we discuss several results concerning constant mean curvature surfaces. We prove that an embedded constant mean curvature disk with Gaussian curvature large at a point contains a multi-valued graph around that point on the scale of |A|2. This generalizes Colding and Minicozzi's result for minimal surfaces. Moreover, we provide examples of CMC surfaces containing arbitrary large multivalued graphs.
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机译:在本文中,我们讨论了有关恒定平均曲率曲面的几个结果。我们证明高斯曲率在某个点处嵌入的恒定平均曲率圆盘在该点周围| A | 2的比例上包含一个多值图形。这样可以将Colding和Minicozzi的结果推广到最小的表面。此外,我们提供了包含任意大型多值图的CMC曲面的示例。
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