Figure 4.

Some stages along the transition of the symmetric catenoidal shape. In the upper panel, the stages (a–c), are in the subcritical regime $\overline{R}<{\overline{R}}^{†}\approx 1.81$, while the stages in the bottom panel (d–f), are in the supercritical regime $\overline{R}>{\overline{R}}^{†}$. The corresponding behavior of the spontaneous curvature, $\overline{K}\left(\overline{l}\right)$, and the local torque $\overline{m}\left(\overline{l}\right)$, is shown as a function of the arc length $\overline{l}$. Note the flip-flop behavior of these functions as passing the critical value ${\overline{R}}^{†}$.