Isothermic surfaces and conservation laws

2024/01/19 by Francis E. Burstall, Emma Carberry, Burstall, F. E. +5
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2401.10618

openalex publication_date 2024/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For CMC surfaces in 3-dimensional space forms, we relate the moment class of Korevaar--Kusner--Solomon to a second cohomology class arising from the integrable systems theory of isothermic surfaces. In addition, we show that both classes have a variational origin as Noether currents.

Related

• Links between the integrable systems of CMC surfaces, isothermic surfaces and constrained Willmore surfaces
• Conservation laws for surfaces of constant mean curvature in 3-dimensional space forms
• CMC hierarchy
• CMC hierarchy I: Commuting symmetries and loop algebra
• Discrete CMC surfaces in R³ and discrete minimal surfaces in S³. A discrete Lawson correspondence