Global real analytic angle parameters for Teichmüller spaces

Yoshihide OKUMURA

doi:10.2969/jmsj/04920213

Yoshihide OKUMURA

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JOURNAL FREE ACCESS

1997 Volume 49 Issue 2 Pages 213-229

DOI https://doi.org/10.2969/jmsj/04920213

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Published: 1997 Received: September 09, 1994 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: SUBTITLE Details: Wrong : Dedicated to the memory of Professor Kiyoshi Niino

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) W. Abikoff, The real analytic theory of Teichmüller space, Lecture Notes in Math. 820, Springer-Verlag, Berlin, Heidelberg, New York, 1980.
2) A. F. Beardon, The geometry of discrete groups, Graduate. Texts in Math., 91, Springer-Verlag, New York, Heidelberg, Berlin, 1983.
3) Y, Imayoshi and M. Taniguchi, An introduction to Teichmüller spaces, Springer-Verlag, Tokyo, Berlin, Heidelberg, New York, Paris, Hong Kong, Barcelona, 1992.
4) L. Keen, Canonical polygons for finitely generated Fuchsian groups, Acta Math., 115 (1966), 1-16.
5) L. Keen, Intrinsic moduli on Riemann surfaces, Ann. of Math., 84 (1966), 404-420.
6) L. Keen, On Fricke moduli, in advances in the theory of Riemann surfaces, (ed. L.V. Ahlfors et al.), Ann. of Math. Stud., 66, Princeton Univ. Press, Princeton, N.J., 1971, pp. 205-224.
7) L. Keen, A correction to “On Fricke moduli”. Proc. Amer. Math. Soc., 40 (1973), 60-62.
8) L. Keen, A rough fundamental domain for Teichmüller spaces, Bull. Amer. Math. Soc., 83 (1977), 1199-1226.
9) Y. Okumura, On the global real analytic coordinates for Teichmüller spaces, J. Math. Soc. Japan, 42 (1990), 91-101.
10) Y. Okumura, Global real analytic length parameters for Teichmüller spaces, Hiroshima Math. J., 26 (1996), 165-179.
11) Y. Okumura, Parametrizations of Teichmüller spaces, XVIth Rolf Nevanlinna Colloquium, (ed. I. Laine and O. Martio), Walter de Gruyter, Berlin, New York, 1996, pp. 181-190.
12) Y. Okumura, On the global real analytic coordinates for Teichmüller spaces II, in preparation.
13) Y. Okumura, A characterization of geometry of Möbius transformations acting on the unit disk by trace inequalities, in preparation.
14) P. Schmutz, Die Parametrisierung des Teichmüllerraumes durch geodätische Längenfunktionen, Comment. Math. Helv., 68 (1993), 278-288.
15) M. Seppälä and T. Sorvali, On geometric parametrization of Teichmüller spaces, Ann. Acad. Sci. Fenn. Ser. AI Math., 10 (1985), 515-526.
16) M. Seppälä and T. Sorvali, Parametrization of Mobius groups acting in a disk, Comment. Math. Helv., 61 (1986), 149-160.
17) M. Seppälä and T. Sorvali, Parametrization of Teichmüller spaces by geodesic length functions, in Holomorphic Functions and Moduli II, (ed. D. Drasin et al.), Mathematical Sciences Research Institute Publications, 11, Springer-Verlag, New York, Berlin, Heidelberg, London, Paris, Tokyo, 1988, pp. 267-284.
18) M. Seppälä and T. Sorvali, Geometry of Riemann surfaces and Teichmüller spaces, Mathematics Studies, 169, North-Holland, Amsterdam, London, New York, Tokyo, 1992.
19) S. A. Wolpert, On the symplectic geometry of deformations of a hyperbolic surface, Ann. of Math., 117 (1983), 207-234.
20) S. A. Wolpert, Geodesic length functions and the Nielsen problem, J. Differential Geom., 25 (1987), 275-296.

Right : [1] W. Abikoff, The real analytic theory of Teichmüller space, Lecture Notes in Math. 820, Springer-Verlag, Berlin, Heidelberg, New York, 1980.
[2] A. F. Beardon, The geometry of discrete groups, Graduate Texts in Math., 91, Springer-Verlag, New York, Heidelberg, Berlin, 1983.
[3] Y. Imayoshi and M. Taniguchi, An introduction to Teichmüller spaces, Springer-Verlag, Tokyo, Berlin, Heidelberg, New York, Paris, Hong Kong, Barcelona, 1992.
[4] L. Keen, Canonical polygons for finitely generated Fuchsian groups, Acta Math., 115 (1966), 1-16.
[5] L. Keen, Intrinsic moduli on Riemann surfaces, Ann. of Math., 84 (1966), 404-420.
[6] L. Keen, On Fricke moduli, in advances in the theory of Riemann surfaces, (ed. L. V. Ahlfors et al.), Ann. of Math. Stud., 66, Princeton Univ. Press, Princeton, N. J., 1971, pp. 205-224.
[7] L. Keen, A correction to “On Fricke moduli”, Proc. Amer. Math. Soc., 40 (1973), 60-62.
[8] L. Keen, A rough fundamental domain for Teichmüller spaces, Bull. Amer. Math. Soc., 83 (1977), 1199-1226.
[9] Y. Okumura, On the global real analytic coordinates for Teichmüller spaces, J. Math. Soc. Japan, 42 (1990), 91-101.
[10] Y. Okumura, Global real analytic length parameters for Teichmüller spaces, Hiroshima Math. J., 26 (1996), 165-179.
[11] Y. Okumura, Parametrizations of Teichmüller spaces, XVIth Rolf Nevanlinna Colloquium, (ed. I. Laine and O. Martio), Walter de Gruyter, Berlin, New York, 1996, pp. 181-190.
[12] Y. Okumura, On the global real analytic coordinates for Teichmüller spaces II, in preparation.
[13] Y. Okumura, A characterization of geometry of Möbius transformations acting on the unit disk by trace inequalities, in preparation.
[14] P. Schmutz, Die Parametrisierung des Teichmüllerraumes durch geodätische Längenfunktionen, Comment. Math. Helv., 68 (1993), 278-288.
[15] M. Seppälä and T. Sorvali, On geometric parametrization of Teichmüller spaces, Ann. Acad. Sci. Fenn. Ser. AI Math., 10 (1985), 515-526.
[16] M. Seppälä and T. Sorvali, Parametrization of Möbius groups acting in a disk, Comment. Math. Helv., 61 (1986), 149-160.
[17] M. Seppälä and T. Sorvali, Parametrization of Teichmüller spaces by geodesic length functions, in Holomorphic Functions and Moduli II, (ed. D. Drasin et al.), Mathematical Sciences Research Institute Publications, 11, Springer-Verlag, New York, Berlin, Heidelberg, London, Paris, Tokyo, 1988, pp. 267-284.
[18] M. Seppälä and T. Sorvali, Geometry of Riemann surfaces and Teichmüller spaces, Mathematics Studies, 169, North-Holland, Amsterdam, London, New York, Tokyo, 1992.
[19] S. A. Wolpert, On the symplectic geometry of deformations of a hyperbolic surface, Ann. of Math., 117 (1983), 207-234.
[20] S. A. Wolpert, Geodesic length functions and the Nielsen problem, J. Differential Geom., 25 (1987), 275-296.

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