On the moduli of constant mean curvature cylinders of finite type in the 3-sphere

Abstract

We show that one-sided Alexandrov embedded constant mean curvature cylinders of finite type in the 3-sphere are surfaces of revolution. This confirms a conjecture by Pinkall and Sterling that the only embedded constant mean curvature tori in the 3-sphere are rotational.

arXiv commentExpanded and revised

References in corpus (6)

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• Equivariant harmonic cylinders
• Bäcklund Transformations and Loop Group Actions
• Limit leaves of a CMC lamination are stable
• On the Existence of Minimal Tori in $S^3$ of Arbitrary Spectral Genus
• Minimal surfaces in the three-Sphere by doubling the Clifford Torus

Cited by in corpus (5)

• Deformations of symmetric CMC surfaces in the 3-sphere
• The spectral data for Hamiltonian stationary Lagrangian tori in R^4
• Families of conformal tori of revolution in the 3-sphere
• Bifurcation of constant mean curvature tori in Euclidean spheres
• Bubbletons are not embedded