Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

  • [Ch1] M. Chuaqui, A unified approach to univalence criteria in the disc and simply-connected domains, Proc. Amer. Math. Soc. (to appear). MR 1233965 (95c:30011)
  • [Ch2] -, The Schwarzian derivative and quasiconformal reflections on $ {S^n}$, Ann. Acad. Sci. Fenn. Ser. A I Math. 17 (1992), 315-326. MR 1190327 (94a:53036)
  • [Ne] Z. Nehari, The Schwarzian derivative and schlicht functions, Bull. Amer. Math. Soc. 55 (1949), 545-551. MR 0029999 (10:696e)
  • [Ep] C. Epstein, The hyperbolic Gauss map and quasiconformal reflections, J. Reine Angew. Math. 372 (1986), 96-135. MR 863521 (88b:30029)
  • [O-S1] B. Osgood and D. Stowe, The Schwarzian derivative and conformal mapping of Riemannian manifolds, Duke Math. J. 67 (1992), 57-99. MR 1174603 (93j:53062)
  • [O-S2] -, A generalization of Nehari's univalence criterion, Comment. Math. Helv. 65 (1990), 234-242. MR 1057241 (92a:53015)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 53C21, 53A30, 53C20

Retrieve articles in all journals with MSC: 53C21, 53A30, 53C20

Additional Information

Keywords: Schwarzian derivative, univalence, conformal metric, simple-connectivity, closed geodesic, trace-free Ricci, scalar curvature
Article copyright: © Copyright 1994 American Mathematical Society

American Mathematical Society