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Mean-convex Alexandrov embedded constant mean curvature tori in the 3-sphere (2016)

Hauswirth, L., Kilian, M., Schmidt, M. U.

Oxford University Press

In: Proceedings of the London Mathematical Society

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Publication Date: 2016-03-10

Description: We introduce the moduli space of spectral curves of constant mean curvature (CMC) 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 CMC tori in the 3-sphere are surfaces of revolution.

Print ISSN: 0024-6115

Electronic ISSN: 1460-244X

Topics: Mathematics