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On the growth of fundamental groups of nonpositive curvature manifolds

Published online by Cambridge University Press:  17 April 2009

Yi-Hu Yang
Yi-Hu Yang
Affiliation:
Institute of Applied Mathematics, Academia Sinica, Beijing 100080, Peoples Republic of China.
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Abstract

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Milnor's classic result that the fundamental group of a compact Riemannian manifold of negative sectional curvature has exponential growth is generalised to the case of negative Ricci curvature and non-positive sectional curvature.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 54 , Issue 3 , December 1996 , pp. 483 - 487
Copyright
Copyright © Australian Mathematical Society 1996

References

[1]Milnor, J., ‘A note on curvature and fundamental group’, J. Differential Geom. 2 (1968), 1–7.CrossRefGoogle Scholar
[2]Ding, Q., ‘The Dirichlet Problem at infinity for manifolds of nonpositive curvature’, in Differential Geometry Proceedings Symposium in honor of Su Buchin on his 90th birthday (World Sci. Publ. Co., 1993), pp. 49–58.Google Scholar
[3]Xin, Y.L., ‘Harmonic maps of the bounded symmetric domains’, Math. Ann. 303 (1995), 417–433.CrossRefGoogle Scholar