Ricci curvature and a criterion for simple-connectivity on the sphere

Chuaqui, Martin

doi:10.1090/S0002-9939-1994-1197534-9

Ricci curvature and a criterion for simple-connectivity on the sphere
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Proc. Amer. Math. Soc. 122 (1994), 479-485 Request permission

Abstract:

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

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