Bounding Shortest Closed Geodesics with Diameter on compact 2-dimensional Orbifolds Homeomorphic to $S^2$

Abstract: Length bounded sweepouts give a way to bound the length of the shortest closed geodesic of a closed manifold. In this paper, we generalized 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 proved an inequality for the length of the shortest closed orbifold geodesic in terms of the diameter.