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A Schwarz lemma for complete Riemannian manifolds

Published online by Cambridge University Press:  17 April 2009

Leung-Fu Cheung  and
Pui-Fai Leung
Leung-Fu Cheung
Affiliation:
Department of Mathematics, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong e-mail: malfcheu@hkpu02.polyu.edu.hk
Pui-Fai Leung
Affiliation:
Department of Mathematics, National University of Singapore, Kent RidgeSingapore 0511 e-mail: matfredl@leonis.nus.sg
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We prove a Schwarz Lemma for conformal mappings between two complete Riemannian manifolds when the domain manifold has Ricci curvature bounded below in terms of its distance function. This gives a partial result to a conjecture of Chua.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 55 , Issue 3 , June 1997 , pp. 513 - 515
Copyright
Copyright © Australian Mathematical Society 1997

References

[1]Chen, Q. and Xin, Y.L., ‘A generalized maximum principle and its applications in geometry’, Amer. J. Math. 114 (1992), 355–366.CrossRefGoogle Scholar
[2]Chua, K.S., ‘A generalisation of Ahlfors-Schwarz lemma to Riemannian geometry’, Bull. Austral. Math. Soc. 51 (1995), 517–520.Google Scholar
[3]Yano, K. and Obata, M., ‘Conformal changes of Riemannian metrics’, J. Differential Geom. 4 (1970), 53–72.CrossRefGoogle Scholar