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math.DG2026
On ideal lemniscates, butterflies, and circular waves
Shinya Okabe, Glen Wheeler
We prove the existence of infinitely many lemniscate-like, butterfly-like, and circular-wave critical points for the length-penalised ideal energy. For the lemniscate and butterfly…
math.DG2026
Homogeneous Sobolev gradient flow of the length functional
Philip Schrader, Glen Wheeler, Valentina Wheeler
The well-known curve shortening flow can be formulated as the gradient flow of the length functional on the space of immersed closed planar curves, where the gradient is taken with…