On the space of minimal surfaces with boundaries
The author's results concern two dimensional minimal surfaces in \({\mathbb{R}}^ n\) which are the image of the unit disc. The main result states that if \(f_ 0\) is a regular minimal surface spanned by a regular analytic Jordan curve, then, in a neighborhood of \(f_ 0\), in the \(C^{r,\alpha}\) topology (0\(\leq r\), \(0<\alpha<1)\), the set of all minimal surfaces is isomorphic to an open set in an infinite dimensional Banach space. The author's method is to define appropriate Banach spaces of functions, obtain certain algebraic properties of these spaces, and use the infinite dimensional version of the inverse function theorem.
scientific article; zbMATH DE number 3864149