The Index Theorem for Minimal Surfaces of Higher Genus

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.