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

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.

This is a revised version of arXiv:0712.0108

References in corpus (2)

• Flows of constant mean curvature tori in the 3-sphere: The equivariant case
• On mean-convex Alexandrov embedded surfaces in the 3-sphere

Cited by in corpus (1)

• Properly embedded minimal annuli in ${\mathbb{S}}^2\times \mathbb{R}$