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TEICHMÜLLER DISTANCE FOR ANALYTICALLY FINITE SURFACES IS C2

Published online by Cambridge University Press:  14 October 2002

MARY REES
MARY REES
Affiliation:
Department of Mathematical Sciences, University of Liverpool, Mathematics and Oceanography Building, Peach Street, Liverpool L69 7ZL. maryrees@liv.ac.uk
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Abstract

It is shown that Teichmüller distance for analytically finite surfaces is C2. This extends Earle's classical result of 1977 that the distance is C1. Earle showed that the first derivative is given by a quadratic differential. In order to obtain the C2 result, first, a formula is derived for the second derivative for a generic choice of quadratic differential, and with respect to certain local coordinates on Teichmüller space. Then this formula is interpreted so that it can be seen that the limit exists at non-generic points.

2000 Mathematical Subject Classification: 30F60, 32G15.

Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 85 , Issue 3 , November 2002 , pp. 686 - 716
Copyright
2002 London Mathematical Society

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