2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75468Following on from ``Hyperbolic Plateau problems'' (by the same author), we provide a complete geometric description of solutions to the Plateau problem $(S,ϕ)$ when $S$ is a compact Riemann surface with a finite number of points removed.Differential GeometrySymplectic Geometry53C42; 30F60; 32Q65; 51M10; 53C45; 53D10; 58D10text