On criteria for extremality of Teichmüller mappings

Author:
Guowu Yao

Journal:
Proc. Amer. Math. Soc. **132** (2004), 2647-2654

MSC (2000):
Primary 30C75

Published electronically:
April 21, 2004

MathSciNet review:
2054790

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a Teichmüller self-mapping of the unit disk corresponding to a holomorphic quadratic differential . If satisfies the growth condition (as ), for any given , then is extremal, and for any given , there exists a subsequence of such that

is a Hamilton sequence. In addition, it is shown that there exists with bounded Bers norm such that the corresponding Teichmüller mapping is not extremal, which gives a negative answer to a conjecture by Huang in 1995.

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Additional Information

**Guowu Yao**

Affiliation:
School of Mathematical Sciences, Peking University, Beijing, 100871, People’s Republic of China

Address at time of publication:
Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100080, People’s Republic of China

Email:
wallgreat@lycos.com, gwyao@mail.amss.ac.cn

DOI:
http://dx.doi.org/10.1090/S0002-9939-04-07420-9

Keywords:
Hamilton sequence,
Teichm\"uller mapping,
extremality

Received by editor(s):
December 3, 2002

Received by editor(s) in revised form:
June 5, 2003

Published electronically:
April 21, 2004

Additional Notes:
This research was supported by the “973” Project Foundation of China (Grant No. TG199075105) and the Foundation for Doctoral Programme

Communicated by:
Juha M. Heinonen

Article copyright:
© Copyright 2004
American Mathematical Society