Totally geodesic boundaries are dense in the moduli space

Michihiko FUJII; Teruhiko SOMA

doi:10.2969/jmsj/04930589

Michihiko FUJII, Teruhiko SOMA

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JOURNAL FREE ACCESS

1997 Volume 49 Issue 3 Pages 589-601

DOI https://doi.org/10.2969/jmsj/04930589

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Published: 1997 Received: June 29, 1995 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: CITATION Details: Wrong : 1) P. Bowers and K. Stephenson, The set of circle packing points in the Teichmüller space of a surface of finite conformal type is dense, Math. Proc. Camb. Phil. Soc., 111 (1992), 487-513.
2) R. Brooks, Circle packings and co-compact extensions of Kleinian groups, Invent. Math., 86 (1986), 461-469.
3) M. Fujii, Deformations of a hyperbolic 3-manifold not affecting its totally geodesic boundary, Kodai Math. J., 16 (1993), 441-454.
4) F. Gardiner, Teichmüller theory and quadratic differentials, Wiley Interscience, New York, 1987.
5) J. Hempel, 3-manifolds, Ann. of Math. Studies no. 86, Princeton Univ. Press, Princeton N.J., 1976.
6) Y. Imayoshi and M. Taniguchi, An Introduction to Teichmüller spaces, Springer-Verlag, Tokyo, 1992.
7) W. Jaco, Lectures on three-manifold topology, C.B.M.S. Regional Conf. Ser, in Math. no. 43, Amer. Math. Soc., Providence R.I., 1980.
8) B. Maskit, On Klein's combination theorem III, Advances in the theory of Riemann surfaces (eds. L. Ahlfors et al.), Ann. of Math. Studies no. 66, Princeton Univ. Press, Princeton N. J., 1971, pp. 297-316.
9) C. McMullen, Amenability, Poincaré series and quasiconformal maps, Invent. Math., 97 (1989), 95-127.
10) C. McMullen, Iteration on Teichmüller space, Invent. Math., 99 (1990), 425-454.
11) J. Morgan, On Thurston's uniformization theorem for three-dimensional manifolds, The Smith conjecture (eds. J. Morgan, H. Bass), Academic Press, New York, London, 1984, pp. 37-125.
12) G. Mostow, Quasi-conformal mappings in n-space and the rigidity of hyperbolic space forms, Publ. Math. I.H.E.S., 34 (1968), 53-104,
13) R. Myers, Simple knots in compact, orientable 3-manifolds, Trans. Amer. Math. Soc., 273 (1982), 75-91.
14) W. Thurston, The geometry and topology of 3-manifolds, Lect. Notes, Princeton Univ., 1978.
15) W. Thurston, Three dimensional manifolds, Kleinian groups and hyperbolic geometry, Bull. Amer. Math. Soc., 6 (1982), 357-381.

Right : [1] P. Bowers and K. Stephenson, The set of circle packing points in the Teichmüller space of a surface of finite conformal type is dense, Math. Proc. Camb. Phil. Soc., 111 (1992), 487-513.
[2] R. Brooks, Circle packings and co-compact extensions of Kleinian groups, Invent. Math., 86 (1986), 461-469.
[3] M. Fujii, Deformations of a hyperbolic 3-manifold not affecting its totally geodesic boundary, Kodai Math. J., 16 (1993), 441-454.
[4] F. Gardiner, Teichmüller theory and quadratic differentials, Wiley Interscience, New York, 1987.
[5] J. Hempel, 3-manifolds, Ann. of Math. Studies no. 86, Princeton Univ. Press, Princeton N. J., 1976.
[6] Y. Imayoshi and M. Taniguchi, An Introduction to Teichmüller spaces, Springer-Verlag, Tokyo, 1992.
[7] W. Jaco, Lectures on three-manifold topology, C. B. M. S. Regional Conf. Ser, in Math. no. 43, Amer. Math. Soc., Providence R. I., 1980.
[8] B. Maskit, On Klein's combination theorem III, Advances in the theory of Riemann surfaces (eds. L. Ahlfors et al.), Ann. of Math. Studies no. 66, Princeton Univ. Press, Princeton N. J., 1971, pp. 297-316.
[9] C. McMullen, Amenability, Poincaré series and quasiconformal maps, Invent. Math., 97 (1989), 95-127.
[10] C. McMullen, Iteration on Teichmüller space, Invent. Math., 99 (1990), 425-454.
[11] J. Morgan, On Thurston's uniformization theorem for three-dimensional manifolds, The Smith conjecture (eds. J. Morgan, H. Bass), Academic Press, New York, London, 1984, pp. 37-125.
[12] G. Mostow, Quasi-conformal mappings in n-space and the rigidity of hyperbolic space forms, Publ. Math. I. H. E. S., 34 (1968), 53-104,
[13] R. Myers, Simple knots in compact, orientable 3-manifolds, Trans. Amer. Math. Soc., 273 (1982), 75-91.
[14] W. Thurston, The geometry and topology of 3-manifolds, Lect. Notes, Princeton Univ., 1978.
[15] W. Thurston, Three dimensional manifolds, Kleinian groups and hyperbolic geometry, Bull. Amer. Math. Soc., 6 (1982), 357-381.

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