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 (2)

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

Cited by in corpus (2)

• Non-collapsing for hypersurface flows in the sphere and hyperbolic space
• Rotational Surfaces in S^3 with constant mean curvature