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Projective structures with discrete holonomy representations
Author(s):
Hiroshige
Shiga;
Harumi
Tanigawa
Journal:
Trans. Amer. Math. Soc.
351
(1999),
813-823.
MSC (1991):
Primary 32G15;
Secondary 30F10
MathSciNet review:
1443890
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Abstract:
Let  denote the set of projective structures on a compact Riemann surface  whose holonomy representations are discrete. We will show that each component of the interior of  is holomorphically equivalent to a complex submanifold of the product of Teichmüller spaces and the holonomy representation of every projective structure in the interior of  is a quasifuchsian group.
References:
- [B]
- L. Bers, Holomorphic families of isomorphisms of Möbius groups, J. Math. Kyoto Univ. 26 (1986), 73-76. MR 87j:32067
- [EKK]
- C. Earle, I. Kra and S. Krushkal, Holomorphic Motions and Teichmüller spaces, Trans. Amer. Math. Soc. 343 (1994), 927-948. MR 94h:32035
- [EM]
- C. Earle and C. McMullen, Quasiconformal isotopes, Holomorphic Functions and Moduli II, Springer-Verlag, New York, Berlin, Heidelberg, London, Paris and Tokyo, 1988, pp. 143-154. MR 89c:30002
- [G1]
- W. Goldman, The symplectic nature of fundamental groups of surfaces, Advances in Math. 54 (1984), 200-225. MR 86i:32042
- [G2]
- -, Projective structures with Fuchsian holonomy, J. Diff. Geom 25 (1987), 297-326. MR 88i:57006
- [H]
- D. Hejhal, Monodromy groups and linearly polymorphic functions, Acta Math. 135 (1975), 1-55. MR 57:3380
- [JM]
- D. Johnson and J. Millson, Deformation spaces associated to compact hyperbolic manifolds, Discrete Groups and Analysis, Papers in honor of G. D. Mostow on his 60-th birthday, Progress in Mathematics, vol. 67, Birkhäuser, pp. 48-106. MR 88j:22010
- [Ko]
- S. Kobayashi, Hyperbolic Manifolds and Holomorphic mappings, Marcel Dekker Inc., New York, 1970. MR 43:3503
- [Kr1]
- I. Kra, A generalization of a theorem of Poincaré, Proc. Amer. Math. Soc. 27 (1971), 299- 302. MR 46:347
- [Kr2]
- -, Deformations of Fuchsian groups, Duke Math. J. 36 (1969), 537-546. MR 42:491
- [Kr3]
- -, Deformations of Fuchsian groups II, Duke Math. J. 38 (1971). MR 44:2951
- [L]
- O. Lehto, Univalent functions and Teichmüller spaces, Springer-Verlag, New York, Berlin, Heidelberg, London, Paris and Tokyo, 1985. MR 88f:30073
- [M]
- B. Maskit, On a class of Kleinian groups, Ann. Acad. Sci. Fenn. Ser. A 442 (1969), 1-8. MR 40:5857
- [Sh]
- H. Shiga, Projective structures on Riemann surfaces and Kleinian groups, J. Math. Kyoto Univ. 27 (1987), 433-438. MR 88k:30056
- [Sl]
- Z. Slodkowski, Holomorphic motions and polynomial hulls, Proc. Amer. Math. Soc. 111 (1991), 347-355. MR 91f:58078
- [Su]
- D. Sullivan, On the ergodic theory at infinity of an arbitrary discrete group of hyperbolic motions, Riemann Surfaces and Related Topics: Proceedings of the 1978 Stony Brook Conference, Annals of Math. Studies 97, Princeton, 1981. MR 83f:58032
- [T1]
- H. Tanigawa, Grafting, harmonic maps and projective structures on surfaces, J. Differential Geometry 47 (1997), 399-419. CMP 98:11
- [T2]
- -, Divergence of projective structures and lengths of measured laminations, (preprint).
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Additional Information:
Hiroshige
Shiga
Affiliation:
Department of Mathematics, Tokyo Institute of Technology, Tokyo 152 Japan
Email:
shiga@math.titech.ac.jp
Harumi
Tanigawa
Affiliation:
Graduate School of Polymathematics, Nagoya University, Nagoya 464-01 Japan
Email:
harumi@math.nagoya-u.ac.jp
DOI:
10.1090/S0002-9947-99-02043-7
PII:
S 0002-9947(99)02043-7
Additional Notes:
Research at MSRI is supported by NSF grant #DMS--9022140
Copyright of article:
Copyright
1999,
American Mathematical Society
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