Closed geodesics and non-differentiability of the metric in infinite-dimensional Teichmüller spaces

Author:
Li Zhong

Journal:
Proc. Amer. Math. Soc. **124** (1996), 1459-1465

MSC (1991):
Primary 30C62; Secondary 32G15, 14H15

MathSciNet review:
1301053

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we construct a closed geodesic in any infinite-

dimensional Teichmüller space. The construction also leads to a proof of non-differentiability of the metric in infinite-dimensional Teichmüller spaces, which provides a negative answer to a problem of Goldberg.

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Additional Information

**Li Zhong**

Affiliation:
Department of Mathematics, Peking University, Beijing 100871, People’s Republic of China

Email:
liz@bepc2.ihep.ac.cn

DOI:
https://doi.org/10.1090/S0002-9939-96-03164-4

Keywords:
Quasiconformal mappings,
Teich\-m\"{u}l\-ler spaces

Received by editor(s):
August 8, 1994

Received by editor(s) in revised form:
October 14, 1994

Additional Notes:
Supported in part by the NSF Grant (Tian-yuan) of China.

Communicated by:
Albert Baernstein II

Article copyright:
© Copyright 1996
American Mathematical Society