Abstract
In 1981 R. Böhme and A. Tromba proved an index theorem for branched minimal surfaces of disk type in Euclidean space ℝ n . One of the consequences of their result is the finiteness of the number of branched minimal disks spanning a contour in general position. Later Tomi and Tromba proved an index theorem for minimal surfaces of higher topological type spanning one boundary contour. In the present chapter these two index theorems are derived. To present the details one needs here as well as in Chapters 4 and 6 a number of notations and theorems from Teichmüller theory and Global analysis; either detailed references are given or results are proved on the spot if they cannot easily be found in the literature. Clearly these chapters are profoundly influenced by ideas of S. Smale and his approach to global nonlinear analysis. Therefore these results can be viewed as a truly nonlinear application of Global analysis.
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