PL-least area 2-orbifolds and its applications to 3-orbifolds (Q2731409)

The authors develop the orbifold analogue of the Jaco-Rubinstein theory of PL-least area surfaces in 3-manifolds, which is used in basic topological results of 3-orbifolds. As an application, the authors prove the loop theorem, Dehn's lemma and the sphere theorem for good orbifolds. The results of this paper are also used by the authors in [Kyushu J. Math. 54, No. 2, 371-401 (2000; Zbl 0961.57013)] for an orbifold version of Waldhausen's theorem, as well as in [Topology Appl. 95, No. 2, 129-153 (1999; Zbl 0924.57013)], where they prove a theorem about geometric realizations of splittings of the fundamental group.