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

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.