Constant mean curvature surfaces, harmonic maps and integrable systems
- 122 Seiten
- 5 Lesestunden
Inhaltsverzeichnis1 Introduction: Surfaces with prescribed mean curvature.2 From minimal surfaces and CMC surfaces to harmonic maps.2.1 Minimal surfaces.2.2 Constant mean curvature surfaces.3 Variational point of view and Noether’s theorem.4 Working with the Hopf differential.4.1 Appendix.5 The Gauss-Codazzi condition.5.1 Appendix.6 Elementary twistor theory for harmonic maps.6.1 Appendix.7 Harmonic maps as an integrable system.7.1 Maps into spheres.7.2 Generalizations.7.3 A new setting: loop groups.7.4 Examples.8 Construction of finite type solutions.8.1 Preliminary: the Iwasawa decomposition (for)..8.2 Application to loop Lie algebras.8.3 The algorithm.8.4 Some further properties of finite type solutions.9 Constant mean curvature tori are of finite type.9.1 The result.9.2 Appendix.10 Wente tori.10.1 CMC surfaces with planar curvature lines.10.2 A system of commuting ordinary equations.10.3 Recovering a finite type solution.10.4 Spectral curves.11 Weierstrass type representations.11.1 Loop groups decompositions.11.2 Solutions in terms of holomorphic data.11.3 Meromorphic potentials.11.4 Generalizations.
