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A rigidity theorem for discrete groups

Published online by Cambridge University Press:  17 April 2009

Wen-Haw Chen  and
Jyh-Yang Wu
Wen-Haw Chen
Affiliation:
Department of Mathematics, Tunghai University, Taichung 40704, Taiwan, e-mail: [email protected]
Jyh-Yang Wu
Affiliation:
Department of Mathematics, National Chung-Cheng University, Chai-Yi 621, Taiwan, e-mail: [email protected]
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This work considers the discrete subgroups of group of isometries of an Alexandrov space with a lower curvature bound. By developing the notion of Hausdorff distance in these groups, a rigidity theorem for the close discrete groups was proved.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 73 , Issue 1 , February 2006 , pp. 1 - 8
Copyright
Copyright © Australian Mathematical Society 2006

References

Referenes

[1]Burago, Y., Gromov, M. and Perelman, G., ‘A.D. Aleksandrov spaces with curvature bounded below’, Uspehi Mat. Nauk 47 (1992), 3–51. Translation in Russian Math. Surveys 47 (1992) 1–58.Google Scholar
[2]Chen, W.-H., ‘Finite group actions on compact negatively curved manifolds’, Arch. Math. 77 (2001), 430–433.CrossRefGoogle Scholar
[3]Cheeger, J. and Colding, T. H., ‘On the structure of spaces with Ricci curvature bounded from below’, J. Diff. Geom. 46 (1997), 406–480.Google Scholar
[4]Fukaya, K. and Yamaguchi, T., ‘Isometry groups of singular spaces’, Math. Z. 216 (1994), 31–44.CrossRefGoogle Scholar
[5]Gromov, M., Metric structures for Riemannian and non-Riemannian spaces, Progress in Mathematics 152 (Birkhauser Boston Inc., Boston, 1999).Google Scholar
[6]Perelman, G., ‘Aleksandrov spaces with curvature bounded from below II’, (preprint).Google Scholar
[7]Petersen V, P., ‘Gromov-Hausdorff convergence of metric spaces’, in Differential Geometry, (Yau, S.-T and Green, R., Editors), Proc. Symp. Pure. Math. 54 (American Mathematical Society, Providence, RI, 1993), pp. 489–504.Google Scholar
[8]Ratcliffe, J., Foundations of hyperbolic manifolds, Graduate Texts in Mathematics 149 (Springer-Verlag, New York, 1994).CrossRefGoogle Scholar
[9]Wei, G., ‘Examples of complete manifolds of positive Ricci curvature with nilpotent isometry groups’, Bull. Amer. Math. Soc. 19 (1988), 311–313.CrossRefGoogle Scholar