# The Index Theorem for Minimal Surfaces of Higher Genus

Share this page
*F. Tomi; A. J. Tromba*

#### Table of Contents

# Table of Contents

## The Index Theorem for Minimal Surfaces of Higher Genus

- Contents v6 free
- §0 Introduction 18 free
- §1 The Differential Geometric Approach to Teichmuller Theory 411 free
- 2 Minimal Surfaces of Higher Genus as Critical Points of Dirichlet's Functional 1522
- §3 Review of Some Basic Results in Riemann Surface Theory 2330
- §4 Vector Bundles over Teichmuller Space 2936
- §5 Minimal Surfaces of Higher Genus as the Zeros of a Vector Field and the Conformality Operators 3542
- §6 The Corank of the Partial Conformality Operators 3946
- §7 The Corank of the Complete Conformality Operators 4855
- §8 Manifolds of Harmonic Surfaces of Prescribed Branching 5158
- §9 The Index Theorem 5764
- Appendix I A Supplement to the Boundary Regularity Theorems for Minimal Surfaces 7380
- Appendix II Maximal Ideals in Sobolev Algebras of Holomorphic Functions 7582
- References 7784