A uniqueness theorem for minimal surfaces in \(S^ 3\)
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.
scientific article; zbMATH DE number 4000886