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.
CITATION STYLE
Hauswirth, L., Kilian, M., & Schmidt, M. U. (2015). Mean-convex Alexandrov embedded constant mean curvature tori in the 3-sphere. Proceedings of the London Mathematical Society, 112(3), 588–622. https://doi.org/10.1112/plms/pdw002
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