Branched immersions between 2-manifolds of higher topological type

In this paper, branched immersions between compact orientable 2-manifolds are considered. Branched immersions are smooth maps whose only singularities are branch points, i.e., points of the domain where the map is locally topologically equivalent to z -> z r (r = 2,3, ) Originally these maps were studied in connection with Douglas' solution to Plateau's problem.