RICCI CURVATURE AND A CRITERION FOR SIMPLE-CONNECTIVITY ON THE SPHERE

From the recent work of Osgood and Stowe on the Schwarzian derivative for conformal maps between Riemannian manifolds we derive a sharp suff icient condition for a domain on the sphere to be simply-connected. We show further that a less restrictive form of the condition yields a u niform lower bound for the length of closed geodesics.