IJPAM: Volume 25, No. 1 (2005)

CURVATURE, DISCRETE GROUPS AND
HAUSDORFF DISTANCE

Wen-Haw Chen
Department of Mathematics
Tunghai University
No. 181, Section 3, Taichung-Kam Road
Taichung, 407-04, TAIWAN, R.O.C.
e-mail: whchen@thu.edu.tw


Abstract.In this short note we develop the notion of Hausdorff distance between the discrete subgroups of the isometry group on a simply connected Riemannian manifold with lower curvature bounds. We prove a rigidity theorem to show that close geometric structures will imply close group structures.

Received: August 3, 2005

AMS Subject Classification: 53C20, 57S25

Key Words and Phrases: curvature, discrete groups, Hausdorff distance

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 25
Issue: 1