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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Author: Martin Chuaqui
Journal: Proc. Amer. Math. Soc. 122 (1994), 479-485
MSC: Primary 53C21; Secondary 53A30, 53C20
MathSciNet review: 1197534
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1197534-9
PII: S 0002-9939(1994)1197534-9
Keywords: Schwarzian derivative, univalence, conformal metric, simple-connectivity, closed geodesic, trace-free Ricci, scalar curvature
Article copyright: © Copyright 1994 American Mathematical Society