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.

Expanded and revised

References in corpus (3)

• 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 (1)

• Families of conformal tori of revolution in the 3-sphere