Complete minimal surfaces lying in simple subsets of \(\mathbb R^3\) (Q5940264)

A result due to \textit{N. Nadirashvili} [Invent. Math. 126, 457-465 (1996; Zbl 0881.53053)] asserts the existence of a complete and bounded minimal surface in \({\mathbb R}^3\). Different authors have extended this result. In this paper, the author proves the existence of three complete minimal surfaces in \({\mathbb R}^3\) lying in domains of Euclidean space: first, an orientable singly periodic surface in a cylinder; second, a nonorientable Möbius strip inside a ball; and finally, an orientable singly periodic surface in a halfspace, but not a slab and transverse to each horizontal plane.