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ON INFINITESIMAL TEICHMÜLLER SPACE

Part of: Geometric function theory

Published online by Cambridge University Press:  01 October 2008

FAN JINHUA  and
CHEN JIXIU
FAN JINHUA*
Affiliation:
Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing, 210094, People’s Republic of China (email: jinhuafan@hotmail.com)
CHEN JIXIU
Affiliation:
School of Mathematical Sciences, Fudan University, Shanghai, 200433, People’s Republic of China
*
✉For correspondence; e-mail: jinhuafan@hotmail.com
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Abstract

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Much research has been done on the geometry of Teichmüller space and Hamilton sequences of extremal Beltrami differentials. This paper discusses some problems concerning infinitesimal Teichmüller geodesic discs and Hamilton sequences of extremal Beltrami differentials in the tangent space of an infinite-dimensional Teichmüller space.

Keywords

infinitesimal Teichmüller spacegeodesic discHamilton sequence

MSC classification

Secondary: 30C75: Extremal problems for conformal and quasiconformal mappings, other methods
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 78 , Issue 2 , October 2008 , pp. 293 - 300
Copyright
Copyright © 2008 Australian Mathematical Society

Footnotes

This work was supported by the Chinese NNSF grant no. 10571028.

References

[1]Božin, V., Lakic, N., Marković, V. and Mateljević, M., ‘Unique extremality’, J. Anal. Math. 75 (1998), 299–338.Google Scholar
[2]Fan, J. and Chen, J., ‘On the equivalence of extremal Teichmüller mapping’, Sci. China. Ser. A 51 (2008), preprintGoogle Scholar
[3]Gardiner, F. P., ‘Approximation of infinite dimension Teichmüller spaces’, Trans. Amer. Math. Soc. 282 (1984), 367–383.Google Scholar
[4]Gardiner, F. P., Teichmüller Theory and Quadratic Differentials (Wiley-Interscience, New York, 1987).Google Scholar
[5]Gardiner, F. P. and Lakic, N., Quasiconformal Teichmüller Theory, Mathematical Surveys and Monographs, 76 (American Mathematical Society, Providence, RI, 2000).Google Scholar
[6]Lakic, N., ‘Strebel points’, Contemp. Math. 211 (1997), 417–431.Google Scholar
[7]Li, Z., ‘Strebel differentials and Hamilton sequences’, Sci. China Ser. A 44 (2001), 969–979.CrossRefGoogle Scholar
[8]Li, Z., ‘Geodesics disks in Teichmüller space’, Sci. China Ser. A 48 (2005), 1075–1082.Google Scholar
[9]Shen, Y., ‘On Teichmüller geometry’, Complex Var. Theory Appl. 44 (2001), 73–83.Google Scholar
[10]Shen, Y., ‘A note on Hamilton sequences for extremal Beltrami coefficients’, Proc. Amer. Math. Soc. 129 (2001), 105–109.Google Scholar
[11]Yao, G., ‘Is there always an extremal Teichmüller mapping’, J. Anal. Math. 94 (2004), 363–375.CrossRefGoogle Scholar