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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.AP2026
Well-posedness of the Langmuir film problem
Yoichiro Mori, Shinya Okabe, Koya Sakakibara
We analyze the inviscid Langmuir layer--Stokesian subfluid (ILLSS) model for two-phase Langmuir monolayers coupled to a Stokes flow in the underlying subfluid. Eliminating the bulk…