On the Stability of the CMC Clifford Tori as Constrained Willmore Surfaces

TL;DR

This paper investigates the stability of a family of Clifford tori in the 3-sphere as constrained Willmore surfaces, identifying which are stable critical points among tori of the same conformal type.

Contribution

It provides a detailed stability analysis of Clifford tori as constrained Willmore surfaces, highlighting which tori are stable critical points.

Findings

Certain Clifford tori are stable critical points

Stability depends on the conformal parameters of the tori

The analysis advances understanding of constrained Willmore surface stability

Abstract

The tori $T_r = r S^1 \times s S^1 \subset S^3$, where $r^2 + s^2 = 1$, are constrained Willmore surfaces, i.e. critical points of the Willmore functional among tori of the same conformal type. We compute which of the $T_r$ are stable critical points.