Flows of constant mean curvature tori in the 3-sphere: The equivariant case

Abstract

We present a deformation for constant mean curvature tori in the 3-sphere. We show that the moduli space of equivariant constant mean curvature tori in the 3-sphere is connected, and we classify the minimal, the embedded, and the Alexandrov embedded tori therein. We conclude with an instability result.

v2: 33 pages, 9 figures. Instability result added

Cited by in corpus (5)

• Mean-convex Alexandrov embedded constant mean curvature tori in the 3-sphere
• The spectral curve theory for $(k,l)-$symmetric CMC surfaces
• Whitham Deformations and the Space of Harmonic Tori in ${\mathbb{S}}^3$
• Solutions of the Sinh-Gordon Equation of Spectral Genus Two and constrained Willmore Tori I
• The space of equivariant harmonic tori in the 3-sphere