Abstract
In this paper, we will study the Bers density problem for the asymptotic Teichmüller space of the unit disk. We first observe that Gehring’s spiral domain is asymptotically equivalent to a Jordan domain in the closure of the universal Teichmüller space. We will also show that the asymptotic class of Flinn’s domain is not in the closure of the asymptotic Teichmüller space. This answers in the negative the Bers density problem for the asymptotic Teichmüller space.
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Acknowledgments
The author would like to express his hearty gratitude to the organizers of “The XXIIth Rolf Nevanlinna Colloquium” for inviting him to talk and for their warmhearted hospitality, and to University of Helsinki for warm hospitality and kind support. He thanks Professor Sadayoshi Kojima for financial support. He also thanks the referee for his/her valuable comments.
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Communicated by Gaven J. Martin.
This paper is dedicated to the memory of Professor Frederick W. Gehring.
The author is partially supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Scientific Research (C), 21540177.
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Miyachi, H. Spirals and the Asymptotic Teichmüller Space. Comput. Methods Funct. Theory 14, 609–622 (2014). https://doi.org/10.1007/s40315-014-0072-0
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DOI: https://doi.org/10.1007/s40315-014-0072-0