Constant mean curvature surfaces and integrable equations

Abstract

CONTENTS Introduction Chapter I. Compact surfaces of constant mean curvature 1. Differential equations of constant mean curvature surfaces 2. Sphere. Hopf theorem 3. Torus. Analytic formulation of the problem 4. Surfaces of higher genus Chapter II. Constant mean curvature tori 5. Doubly periodic solutions of the equation 6. The Baker-Akhiezer function. Analytic properties 7. The Baker-Akhiezer function. Explicit formulae 8. Reality 9. Formula for immersion 10. Periodicity conditions 11. Area 12. Wente tori 13. Singular spectral curves Chapter III. Constant mean curvature surfaces in S3 and H3 14. Equations of constant mean curvature surfaces in S3 and H3 15. Constant mean curvature spheres in S3 and H3 16. Constant mean curvature tori in S3 17. Minimal tori in S3 and Willmore tori 18. Constant mean curvature tori in H3 19. Minimal surfaces of higher genus in S3 Appendix. Painlevé planes of constant mean curvature References