**Memoirs of the American Mathematical Society**

1995;
78 pp;
Softcover

MSC: Primary 49; 53; 58;

Print ISBN: 978-0-8218-0352-3

Product Code: MEMO/117/560

List Price: $36.00

AMS Member Price: $21.60

MAA Member Price: $32.40

**Electronic ISBN: 978-1-4704-0139-9
Product Code: MEMO/117/560.E**

List Price: $36.00

AMS Member Price: $21.60

MAA Member Price: $32.40

# The Index Theorem for Minimal Surfaces of Higher Genus

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*F. Tomi; A. J. Tromba*

The question of estimating the number of minimal surfaces that
bound a prescribed contour has been open since Douglas's solution of the
Plateau problem in 1931. In this book, the authors formulate and prove
an index theorem for minimal surfaces of higher topological type
spanning one boundary contour.

#### Readership

Mathematicians working in global analysis and/or minimal surface theory.

#### 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