Embedded constant mean curvature tori in the three-sphere

Abstract

We prove that any constant mean curvature embedded torus in the three dimensional sphere is axially symmetric, and use this to give a complete classification of such surfaces for any given value of the mean curvature.

19 pages, 1 figure, more details in the derivation of formula (31) was added in section 4

References in corpus (3)

• Non-collapsing in mean-convex mean curvature flow
• Embedded minimal tori in S^3 and the Lawson conjecture
• Non-collapsing in fully nonlinear curvature flows

Cited by in corpus (7)

• Conservation laws for surfaces of constant mean curvature in 3-dimensional space forms
• Non-collapsing for hypersurface flows in the sphere and hyperbolic space
• Two-point functions and their applications in geometry
• Rotational Surfaces in S^3 with constant mean curvature
• Alexandrov immersed minimal tori in S^3
• Two-sided non-collapsing curvature flows
• A new characterization of the Clifford torus via scalar curvature pinching