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Bulletin of the American Mathematical Society

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Book Review

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Book Information:

Authors: Ravi S. Kulkarni and Ulrich Pinkall
Title: Conformal geometry
Additional book information: Aspects of Mathematics, Friedr. Vieweg & Sohn, Braunsweig and Wiesbaden, 1988, viii + 236 pp. ISBN 3-528-08982-2.

References [Enhancements On Off] (What's this?)

  • [A] B. N. Apanosov, Nontriviality of Teichmüller space for Kleinian groups in space, Riemann Surfaces and Related Topics, Proceedings of the 1978 Conference at Stony Brook (I. Kra and B. Maskit, eds.), Ann. of Math. Stud. vol. 97, Princeton Univ. Press, Princeton, N.J., 21-31. MR 624802
  • [A2] B. N. Apanosov, On non-connectedness of the space of uniformized conformal structures on hyperbolic manifolds, Institut Mittag-Leffler, Djursholm Report, no. 1, 1989-1990.
  • [B] R. Brooks, The fundamental group and the spectrum of the Laplacian, Comment. Math. Helv. 56 (1981), 581-598. MR 656213
  • [CG] J. P. Conze and Y. Guivarch, Remarques sur la distalité dans les espaces vectoriels, C. R. Acad. Sci. Paris Sér. I Math. 278 (1974), 1083-1086. MR 339108
  • [EM] D. B. A. Epstein and A. Marden, Convex hulls in hyperbolic space, a theorem of Sullivan and measured pleated surfaces, Analytical and Geometrical Aspects of Hyperbolic Space, London Math. Soc. Lecture Note Ser., vol. 111, Cambridge Univ. Press, New York, 1987, pp. 113-254. MR 903852
  • [F] D. Fried, Closed similarity manifolds, Comment. Math. Helv. 55 (1981), 576-582. MR 604714
  • [FL] F. Luo, Triangulations in conformally flat geometry, USCD, preprint.
  • [G] W. Goldman, Conformally flat manifolds with nilpotent holonomy and the uniformization problem for 3-manifolds, Trans. Amer. Math. Soc. 278 (1983), 573-583. MR 701512
  • [GLT] M. Gromov, H. B. Lawson, and W. P. Thurston, Hyperbolic 4-manifolds and conformally flat 3-manifolds, Publ. Math. I.H.E.S. 68 (1988), 27-24. MR 1001446
  • [JM] D. Johnson and J. J. Millson, Deformation spaces associated to compact hyperbolic manifolds, Discrete Groups in Geometry and Analysis, Papers in honor of G. D. Mostow on his sixtieth birthday, Prog. Math., vol. 67 Birkhäuser, Boston, 1987, pp. 48-106. MR 900823
  • [Ka] Y. Kamishima, Conformally flat manifolds whose developing maps are not surjective, Trans. Amer. Math. Soc. 294 (1986), 607-623. MR 825725
  • [Kv] M. Kapovich, Flat conformal structures on 3-manifolds, Novosibirsk preprint, 1989. MR 1025290
  • [KP] M. Kapovich and L. Potyagailo, The absence of Ahlfors'finiteness theorem in higher dimensions, Novosibirsk preprint, 1989.
  • [Ko] C. Kouroniotis, Deformations of hyperbolic structures, Math. Proc. Cambridge Philos. Soc. 98 (1985), 247-261. MR 795891
  • [K1 ] N. Kuiper, On conformally flat spaces in the large, Ann. of Math. 20 (1949), 916-924. MR 31310
  • [K2] N. Kuiper, On compact conformally Euclidean spaces of dimension > 2, Ann. of Math. 52 (1950), 478-490. MR 37575
  • [K3] N. Kuiper, Hyperbolic 4-manifolds and tesselations, Publ. Math. I.H.E.S. 68 (1988), 47-76. MR 1001447
  • [Kl] R. Kulkarni, The principle of uniformization, J. Differential Geom. 13 (1978), 109-138. MR 520605
  • [L] F. Labourie, Surfaces convexes dans l'espace hyperbolique et CP (submitted).
  • [M] S. Matsumoto, Foundations of flat conformal structures, Nihon University, preprint. MR 1208312
  • [N] M. Nori, The Schottky groups in higher dimensions, Proceedings of the Lefschetz Centennial Conference, Contemp. Math., vol. 58, part I, Amer. Math. Soc., Providence, R. I., 1986, pp. 195-197. MR 860414
  • [SY] R. Schoen and S. T. Yau, Conformally flat manifolds, Kleinian groups and scalar curvature, Invent. Math. 92 (1988), 47-72. MR 931204
  • [Sc] G. P. Scott, The geometries of 3-manifolds, Bull. London Math. Soc. 15 (1983), 410-478. MR 705527
  • [Sul] 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 Conference at Stony Brook (I. Kra and B. Maskit, eds.), Ann. of Math. Stud., vol. 97, Princeton Univ. Press, Princeton, N.J., pp. 465-496. MR 624833
  • [St] D. Sullivan and W. Thurston, On manifolds with canonical coordinates, Enseign. Math. (2) 29 (1983), 15-25. MR 702731
  • [T] W. Thurston, The geometry and topology of 3-manifolds, Princeton Univ. lecture notes, 1979.

Review Information:

Reviewer: William M. Goldman
Journal: Bull. Amer. Math. Soc. 23 (1990), 566-575
DOI: https://doi.org/10.1090/S0273-0979-1990-15984-1
American Mathematical Society