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Conformal Geometry and Dynamics

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The Teichmüller space of a countable set of points on a Riemann surface


Authors: Ege Fujikawa and Masahiko Taniguchi
Journal: Conform. Geom. Dyn. 21 (2017), 64-77
MSC (2010): Primary 30F60; Secondary 32G15
DOI: https://doi.org/10.1090/ecgd/301
Published electronically: February 1, 2017
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Abstract: We introduce the quasiconformal deformation space of an ordered countable set of an infinite number of points on a Riemann surface and give certain conditions under which it admits a complex structure via Teichmüller spaces of associated subsurfaces with the complement of the set of points. In a similar fashion, we give another definition of the quasiconformal deformation space of a finitely generated Kleinian group.


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Additional Information

Ege Fujikawa
Affiliation: Department of Mathematics, Chiba University, Inage-ku, Chiba 263-8522, Japan
Email: fujikawa@math.s.chiba-u.ac.jp

Masahiko Taniguchi
Affiliation: Department of Mathematics, Nara Women’s University, Nara 630-8506, Japan
Email: tanig@cc.nara-wu.ac.jp

DOI: https://doi.org/10.1090/ecgd/301
Received by editor(s): August 18, 2016
Received by editor(s) in revised form: January 13, 2017
Published electronically: February 1, 2017
Additional Notes: The first author was partially supported by Grants-in-Aid for Scientific Research (C) Grant No. 25400127
The second author was partially supported by Grants-in-Aid for Scientific Research (C) Grant No. 15K04925
Article copyright: © Copyright 2017 American Mathematical Society