On false branch points of incompressible branched immersions - Gulliver, Robert; Tomi, Friedrich (Manuscripta mathematica, 1989)
We prove that a branched immersion of a surface with boundary into a differentiable manifold has no false branch points (in fact, no ramified points) if the immersion induces an isomorphism of fundamental groups and some other natural hypotheses are satisfied. This result has immediate applications to Plateau's problem.