A uniqueness theorem for minimal surfaces in \(S^ 3\)
type: Item
instance of: scholarly article
title: A uniqueness theorem for minimal surfaces in \(S^ 3\)
zbMATH Open document ID: 0617.53008
author: Makoto Sakaki
published in: Kodai Mathematical Journal
publication date: 1987-01-01T00:00:00Z
review text: In this paper the author proves that if y is a \(C^ 2\)-Jordan curve on a geodesic 2-sphere in \(S^ 3\) belonging to some open hemisphere of \(S^ 3\), then there exists a positive number \(\epsilon\) such that any Jordan curve in \(S^ 3\) which is \(\epsilon\) close to y in the \(C^ 2\)-norm is the boundary curve of a unique compact minimal surface in the open hemisphere. This minimal surface can be represented as a graph over the geodesic 2-sphere.
Mathematics Subject Classification ID: 53A10
zbMATH DE Number: 4000886
zbMATH Keywords: Jordan boundary
zbMATH Keywords: minimal surface
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138037358
OpenAlex ID: W1966198331
cites work: The global behavior of minimal surfaces in \(S^ n\)
cites work: Complete minimal surfaces in \(S^ 3\)
cites work: Uniqueness theorems for minimal surfaces
DOI: 10.2996/KMJ/1138037358
description: scientific article; zbMATH DE number 4000886