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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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: 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: http://dx.doi.org/10.1090/S0002-9939-96-03164-4
PII: S 0002-9939(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