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The index theorem for minimal surfaces of higher genus

About this Title

F. Tomi and A. J. Tromba

Publication: Memoirs of the American Mathematical Society
Publication Year: 1995; Volume 117, Number 560
ISBNs: 978-0-8218-0352-3 (print); 978-1-4704-0139-9 (online)
DOI: https://doi.org/10.1090/memo/0560
MathSciNet review: 1276862
MSC: Primary 58E12; Secondary 49Q05, 53A10, 58B15

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Table of Contents

Chapters

• 0. Introduction
• 1. The differential geometric approach to Teichmüller theory
• 2. Minimal surfaces of higher genus as critical points of Dirichlet’s functional
• 3. Review of some basic results in Riemann surface theory
• 4. Vector bundles over Teichmüller space
• 5. Minimal surfaces of higher genus as the zeros of a vector field and the conformality operators
• 6. The corank of the partial conformality operators
• 7. The corank of the complete conformality operators
• 8. Manifolds of harmonic surfaces of prescribed branching type
• 9. The index theorem
• Appendix I
• Appendix II