2025/03/31 by Joseph Cho, Cho, Joseph, Katrin Leschke +3
Mathematics · #(2020): 53A04 (Primary) 53A31 #58J72 (Secondary) #Advanced Differential Equations and Dynamical Systems #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2503.23891
openalex publication_date 2025/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that every finite type polarised curve in the conformal 2-sphere with a polynomial conserved quantity admits a resonance point, under a non-orthogonality assumption on the conserved quantity. Using this fact, we deduce that every finite type curve polarised by space form arc-length in the conformal 2-sphere admits a resonance point, possibly on a multiple cover.