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Teichmüller distance is not $C^{2+\varepsilon}$

Published online by Cambridge University Press:  13 January 2004

Mary Rees
Mary Rees
Affiliation:
Department of Mathematical Sciences, University of Liverpool, Mathematics and Oceanography Building, Peach Street, Liverpool L69 7ZL. E-mail: [email protected]
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Abstract

The Teichmüller space of a finite-type surface is considered. It is shown that Teichmüller distance is not $C^{2 + \epsilon }$ for any $\epsilon > 0$. Furthermore, Teichmüller distance is not $C^{2 + g}$ for any gauge function $g$ with $\liminf_{u \to 0} g(u)\log (1 / u)=0$.

Keywords

Teichmüller spaceTeichmüller distance30F60
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 88 , Issue 1 , January 2004 , pp. 114 - 134
Copyright
2004 London Mathematical Society

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