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On analytic properties of deformation spaces of Kleinian groups


Author: Hiroshige Shiga
Journal: Trans. Amer. Math. Soc. 368 (2016), 6627-6642
MSC (2010): Primary 32G15; Secondary 30C40, 30F60, 37F30
DOI: https://doi.org/10.1090/tran/6563
Published electronically: November 18, 2015
MathSciNet review: 3461045
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Abstract: Let $ G_0$ be a non-elementary Kleinian group. We consider the deformation space of $ D(G_0)$, the space of quasiconformal deformations of $ G_0$, and its complex analytic properties. We show some analytic structures of $ D(G_0)$ which are improvements of results by Bers, Kra, Maskit and McMullen. In particular, we clarify that the structures for Kleinian groups with non-simply connected components are different from those for Kleinian groups without non-simply connected components.


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Additional Information

Hiroshige Shiga
Affiliation: Department of Mathematics, Tokyo Institute of Technology, O-okayama, Meguro-ku Tokyo, Japan
Email: shiga@math.titech.ac.jp

DOI: https://doi.org/10.1090/tran/6563
Keywords: Kleinian groups, quasiconformal maps, Teichm\"uller spaces, holomorphic convexity
Received by editor(s): December 19, 2013
Received by editor(s) in revised form: September 2, 2014
Published electronically: November 18, 2015
Additional Notes: The author was partially supported by the Ministry of Education, Science, Sports and Culture, Japan; Grant-in-Aid for Scientific Research (B), 22340028, 2010–2014.
Article copyright: © Copyright 2015 American Mathematical Society