Embedded minimal disks with a free boundary on a polyhedron in \({\mathbb R}^ 3\)
We show that a convex polyhedron in Euclidean 3-space bounds an embedded minimal surface meeting this polyhedron orthogonally along its boundary. The minimal surface is nontrivial in the sense that it does not coincide with a face and does not contain an edge of the polyhedron in its boundary. The proof is based on previous results of the author for smooth free boundaries, a blow-up argument, and barrier constructions utilizing catenoids.
scientific article; zbMATH DE number 4030384