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arXiv · 1309.4278

Mean-convex Alexandrov embedded constant mean curvature tori in the 3-sphere

L. Hauswirth·M. Kilian·M. U. Schmidt
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Abstract

We introduce the moduli space of spectral curves of constant mean curvature (\cmc\hspace{-5pt}) cylinders of finite type in the round unit 3-sphere. The subset of spectral curves of mean-convex Alexandrov embedded cylinders is explicitly determined using a combination of integrable systems and geometric analysis techniques. We prove that these cylinders are surfaces of revolution. As a consequence all mean-convex Alexandrov embedded {\sc{cmc}} tori in the 3-sphere are surfaces of revolution.

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L. Hauswirth, M. Kilian, M. U. Schmidt. 2015-04-09. Mean-convex Alexandrov embedded constant mean curvature tori in the 3-sphere. https://doi.org/10.1112/plms%2Fpdw002

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