On the space of minimal surfaces with boundaries
type: Item
instance of: scholarly article
title: On the space of minimal surfaces with boundaries
zbMATH Open document ID: 0543.58014
author: Miyuki Koiso
published in: Osaka Journal of Mathematics
publication date: 1983-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 58E12
Mathematics Subject Classification ID: 53A10
zbMATH DE Number: 3864149
zbMATH Keywords: minimal surfaces
zbMATH Keywords: Banach spaces of functions
zbMATH Keywords: inverse function theorem
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3864149