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Journal of the London Mathematical Society Advance Access originally published online on October 11, 2009
Journal of the London Mathematical Society 2009 80(3):716-728; doi:10.1112/jlms/jdp052
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© 2009 London Mathematical Society

Riemann mappings of invariant components of Kleinian groups

Hiroshige Shiga

Department of Mathematics
Tokyo Institute of Technology
Tokyo
Japan

In this paper, we shall investigate complex analytic properties of Riemann mappings of simply connected invariant components of Kleinian groups. In particular, we consider the growth of the derivatives of Riemann mappings to understand Kleinian groups that are quasi-Fuchsian groups, regular b-groups and Kleinian groups with bounded geometry.

2000 Mathematics Subject Classification 30F40 (primary), 30C35 (secondly).

This research was partially supported by Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Scientific Research (A), 2005–2009, 17204010.

Received August 22, 2008; revised June 30, 2009; published online October 11, 2009.


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