A complete minimal Klein bottle in \(\mathbb{R}^ 3\)
The author studies complete nonorientable minimal surfaces in \(\mathbb{R}^ 3\) with finite total curvature. For a long time, the only known nonorientable minimal surface was Henneberg's surface, which is not regular. Later, Meeks exhibited a minimal Möbius strip with total curvature \(C= -6\pi\). In this paper, a new important example is constructed, a minimal Klein bottle with \(C= -8\pi\). Geometrically, this surface is obtained by attaching a Klein bottle to the Enneper surface. In a forthcoming paper, the author will publish a uniqueness theorem and a classification of all complete minimal surfaces with \(C> -10\pi\).
scientific article; zbMATH DE number 495435
scientific article