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

TL;DR

This paper studies the structure and classification of equivariant constant mean curvature tori in the 3-sphere, revealing their connected moduli space and properties like minimality, embeddedness, and stability.

Contribution

It introduces a deformation method, proves the connectedness of the moduli space, and classifies various types of equivariant CMC tori in the 3-sphere.

Findings

Moduli space of equivariant CMC tori in S^3 is connected

Classification of minimal, embedded, and Alexandrov embedded tori

An instability result for these tori

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.