Bounding shortest closed geodesics with diameter on compact 2-dimensional orbifolds homeomorphic to $S^2$

Abstract

Length-bounded sweepouts provide a method for bounding the length of the shortest closed geodesic of a closed manifold. In this paper, we generalize this approach to the case of compact 2-dimensional orbifolds homeomorphic to $S^2$ as well as compact 2-dimensional orbifolds with finite orbifold fundamental groups. We establish an inequality for the length of the shortest closed orbifold geodesic in terms of the diameter.