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We establish sharp universal upper bounds on the length of the shortestclosed geodesic on a punctured sphere with three or four ends endowed with acomplete Riemannian metric of finite area. These sharp curvature-free upperbounds are expressed in terms of the area of the punctured sphere. In bothcases, we describe the extremal metrics, which are modeled on the Calabi-Crokesphere or the tetrahedral sphere. We also extend these optimal inequalities forreversible and non-necessarily reversible Finsler metrics. In this setting, weobtain optimal bounds for spheres with a larger number of punctures. Finally,we present a roughly asymptotically optimal upper bound on the length of theshortest closed geodesic for spheres/surfaces with a large number of puncturesin terms of the area.

Sharp upper bounds on the length of the shortest closed geodesic on complete punctured spheres of finite area