Journal of Geometric Analysis
Weierstrass representations are given for minimal surfaces that have free boundaries on two planes that meet at an arbitrary dihedral angle. The contact angles of a surface on the planes may be different. These surfaces illustrate the behavior of soapfilms in convex and nonconvex corners. They can also be used to show how a boundary wire can penetrate a soapfilm with a free end, as in the overhand knot surface. They should also cast light on the behavior of capillary surfaces.
K. Brakke, Minimal Surfaces, Corners, and Wires, J. Geom. Anal. vol. 2 no. 1 (1992), 11-36.