Memoirs of the American Mathematical Society 1995; 78 pp; softcover Volume: 117 ISBN10: 0821803522 ISBN13: 9780821803523 List Price: US$36 Individual Members: US$21.60 Institutional Members: US$28.80 Order Code: MEMO/117/560
 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. The Index Theorem for Minimal Surfaces of Higher Genus describes, in terms of Fredholm Index, a rough measure on the set of curves bounding minimal surfaces of prescribed branching type and genus. Readership Mathematicians working in global analysis and/or minimal surface theory. Table of Contents  Introduction
 The differential geometric approach to Teichmüller theory
 Minimal surfaces of higher genus as critical points of Dirichlet's functional
 Review of some basic results in Riemann surface theory
 Vector bundles over Teichmüller space
 Minimal surfaces of higher genus as the zeros of a vector field and the conformality operators
 The corank of the partial conformality operators
 The corank of the complete conformality operators
 Manifolds of harmonic surfaces of prescribed branching type
 The index theorem
 Appendix I. A supplement to the boundary regularity theorems for minimal surfaces
 Appendix II. Maximal ideals in Sobolev algebras of holomorphic functions
 References
