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

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...

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Bibliographic Details
Published in:Proceedings of the London Mathematical Society 2016-03, Vol.112 (3), p.588-622
Main Authors: Hauswirth, L., Kilian, M., Schmidt, M. U.
Format: Article
Language:English
Subjects:
Mathematics
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Summary: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.
ISSN:0024-6115
1460-244X
DOI:10.1112/plms/pdw002