Biholomorphic isomorphisms between Teichmüller curves

Journal d'Analyse Mathematique

Volumn 100, Issue , 2006, Pages 191-209

  Shen, Yuliang ^a  

^a SOOCHOW UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34247537132     PISSN: 00217670     EISSN: 15658538     Source Type: Journal    
DOI: 10.1007/BF02916760     Document Type: Article

References (31)

1. L. V. Ahlfors, On quasiconformal mappings, J. Anal. Math. 3 (1953/4), 1-58.
2. L. Bers, Uniformization, moduli, and Kleinian groups, Bull. London Math. Soc. 4 (1972). 257-300.
3. L. Bers, Fiber spaces over Teichmüller spaces, Acta Math. 130 (1973), 89-126.
4. L. Bers, Finite dimensional Teichmüller spaces and generalizations. Bull. Amer. Math. Soc. 5 (1981), 131-172.
5. J. S. Birman, The algebric structure of surface mapping class group, in Discrete Groups and Automorphic Functions, (W. J. Harvey, ed.), Academic Press, London, 1977, pp. 163-198.
6. H. Cartan, Quotient d'un espace analytique par un group d' automorphismes, in Algebric Geometry and Algebraic Topology, Princeton University Press, Princeton, NJ, 1957, pp. 90-102.
7. Y. Cai and Y. Shen, An isomorphism theorem for Teichmüller curves, Science in China 49 (2006), 577-586.
8. A. Duma, Die Automorphismengruppe der universellen Familie kompakter Riemannscher Flaechen vom Geschlecht g ≥ 3, Manuscripta Math. 17 (1975), 309-315.
9. C. J. Earle and R. S. Flower, Holomorphic families of open Riemann surfaces, Math. Ann. 270 (1985), 249-273.
10. C. J. Earle and F. P. Gardiner, Geometric isomorphisms between infinite dimensional Teichmüller spaces, Tran. Amer. Math. Soc. 348 (1996), 1163-1190.
11. C. J. Earle, F. P. Gardiner and N. Lakic, Teichmüller spaces with asymptotic conformal equivalence, preprint 1995
12. C. J. Earle and I. Kra, On holomorphic mappings between Teichmüller spaces, in Contributions to Analysis, Academic Press, New York, 1974, pp. 107-124.
13. C. J. Earle and I. Kra, On sections of some holomorphic families of closed Riemann surfaces, Acta Math. 137 (1976), 49-79.
14. 1 holomorphic quadratic differentials on Riemann surfaces of finite type, Duke Math. J. 120 (2003), 433-440.
15. A. Epstein, Effectiveness of Teichmüller modular groups, in In the Tradition of Ahlfors and Bers, Contemp. Math. 256 (2000), 69-74.
16. D. B. A. Epstein, Curves on 2-manifolds and isotopies, Acta Math. 115 (1966), 83-107.
17. F. P. Gardiner, Teichmüller Theory and Quadratic Differentials, Wiley-Interscience, New York, 1987.
18. A. Grothendieck, Techniques de construction en géométrie analytique, Sem. Cartan, ( 1960/61 ), expose 17.
19. Y. Hu and Y. Shen, Isomorphisms of fiber spaces over Teichmüller spaces, Science in China 49 (2006), 877-892.
20. I. Kra, Canonical mappings between Teichmüller spaces, Bull. Amer. Math. Soc. 4 (1981), 143-179.
21. I. Kra, On the Nielsen-Thurston-Bers type of some self-maps of Riemann surfaces, Acta Math. 146 (1981), 231-270.
22. N. Lakic, An isometry theorem for quadratic differentials on Riemann surfaces of finite genus, Tran. Amer. Math. Soc. 349 (1997), 2951-2967.
23. O. Lehto, Univalent Functions and Teichmüller Spaces, Springer-Verlag, New York, 1987.
24. V. Markovic, Biholomorphic maps between Teichmüller spaces, Duke Math. J. 120 (2003), 403-431.
25. K. Matsuzaki, Inclusion relations between the Bers embeddings of Teichmüller spaces, Israel J. Math. 140 (2004), 113-123.
26. S. Nag, Nongeodosic disks embedded in Teichmüller spaces. Amer. J. Math. 104 (1982), 399-408.
27. S. Nag, The Complex Analytic Theory of Teichmüller Spaces, Wiley-Interscience, New York, 1988.
28. G. Riera, Semi-direct products of Fuchsian groups and uniformisation, Duke Math. J. 44 (1977), 291-304.
29. H. L. Royden, Automorphisms and isometries of Teichmüller space, in Advances in the Theory of Riemann Surfaces, Princeton University Press, Princeton , NJ, 1971, pp. 369-383.
30. Y. Shen, Fiber spaces over Teichmüller spaces for Fuchsian groups with elliptic elements, Math. Z., to appear.
31. C. Zhang, On isomorphisms of Bers fiber spaces, Ann. Acad. Sci. Fenn. Math. 22 (1997), 255-274.