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Geodesic uniqueness and derivatives of Bers projection

Published online by Cambridge University Press:  17 April 2009

Hui Guo
Hui Guo
Affiliation:
Department of Mathematical Education, Normal College, Shenzhen University, Shenzhen, Guangdong 518060, Peoples Republic of China Institute of Mathematics, Chinese Academy of Sciences, Beijing 100080, Peoples Republic of China, e-mail: hguo@szu.edu.cn, szuhguo@hotmail.com
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Abstract

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In this paper, we discover a sufficient and necessary condition under which two geodesic segments joining the base point and another point in an infinite-dimensional Teichmüller space are the same.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 67 , Issue 1 , February 2003 , pp. 145 - 162
Copyright
Copyright © Australian Mathematical Society 2003

References

REFERENCES

[1]Busemann, H., The geometry of geodesics (Academic Press, New York, 1955).Google Scholar
[2]Gaier, D., Lectures on complex approximation (Birkhäuser, Boston, 1987).CrossRefGoogle Scholar
[3]Gardiner, F.P., ‘On completing triangles in infinite dimensional Teichmüller spaces’, Complex Variables Theory Appl. 10 (1988), 237–247.Google Scholar
[4]Imayoshi, Y. and Taniguchi, M., An introduction to Teichmüller spaces (Spring-Verlag. Tokyo, 1992).CrossRefGoogle Scholar
[5]Kravetz, S., ‘On the geometry of Teichmüller spaces and the structure of their modular groups’, Ann. Acad. Sci. Fenn. Ser. A I Math. 278 (1959), 1–35.Google Scholar
[6]Lehto, O., Univalent functions and Teichmüller spaces, Graduate Texts in Mathematics 109 (Springer-Verlag, New York, 1987).CrossRefGoogle Scholar
[7]Li, Z., Quasiconformal mappings and their applications in the theory of Riemann surfaces, (in Chinese)(Scientific Press, Beijing, 1988).Google Scholar
[8]Li, Z., ‘Non-uniqueness of geodesics in infinite dimensional Teichmüller spaces’, Complex variables Theory Appl. 16 (1991), 261–272.Google Scholar
[9]Li, Z., ‘Non-uniqueness of geodesics in infinite dimensional Teichmüller spaces (II)’. Ann. Acad. Sci. Fenn. Ser. A I Math. 18 (1993), 355–367.Google Scholar
[10]O'Byrne, B., On Finsler geometry and applications to Teichmüller spaces, Ann. of Math. Studies 66 (Princeton University Press, Princeton, NJ, 1971), pp. 317–328.Google Scholar
[11]Shen, Y., ‘Non-uniqueness of geodesics in the universal Teichmüller spaces’, Adv. in Math. (China) 24 (1995), 237–243.Google Scholar
[12]Strebel, K., ‘Extremal quasiconformal mappings’, Resultate Math. 10 (1986), 168–210.CrossRefGoogle Scholar
[13]Tanigawa, H., ‘Holomorphic families of geodesic discs in infinite dimensional Teichmüller spaces’, Nagoya Math. J. 127 (1992), 117–128.CrossRefGoogle Scholar