Elastic curves and Willmore Hopf-Tori

Whitham deformation Flow of elastic curves in S 2Properties of elastic curves◮ Wave-like elastica bifurcate off great circles.◮ Free elastic curves (no area or length constraint) are wave-like.◮ Orbit-like elastica bifurcate off non-great, at least twicewrapped circles. They are never embedded, and always end ina singular limit.◮ Some wave-like families deform between ω 1 –wrapped andω 2 –wrapped equators. Denote the the lobe number by l.Then for l/ω 1 ∈ (1/2, 1) ∩ Q haveω 1 + ω 2 = 2l .◮ Free elastica are only contained in families withl/ω 1 ∈ (1/2, 1/ √ 2).