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

2007/12/03 by Martin Kilian, Kilian, M., Martin Schmidt +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.0712.0108

openalex publication_date 2007/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Limit leaves of a CMC lamination are stable
• The unknottedness of minimal embeddings
• Bäcklund Transformations and Loop Group Actions

Related

• Embedded constant mean curvature tori in the three-sphere
• Rotationally invariant constant mean curvature surfaces in homogeneous 3-manifolds
• Families of conformal tori of revolution in the 3-sphere
• Rotational Surfaces in S³ with constant mean curvature
• Alexandrov immersed minimal tori in S³