Zum Aufbau einfach zusammenhängender Minimalflächen - besonders über ihre Instabilität und Häufung. (About the structure of simply connected minimal surfaces with emphasis on instability and clustering) (Q1084334)

The author gives some kind of rectifiable Jordan curve \(\gamma\) in \({\mathbb{R}}^ 3\), such that (1) \(\Gamma\) bounds an oriented minimal surface \(S_ 0\) of disk type, which is unstable; and (2) a sequence of minimal surfaces \(S_ n(n=1,2,...)\) of the same type as \(S_ 0\) spanning \(\gamma\) cluster at \(S_ 0\) in a natural topology. A crux of the proof lies in constructing infinitely many stationary points of the Dirichlet integral functional, which furnishes it with distinct and no absolutely minimal values.