Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)



Discrete conformal groups and measurable dynamics

Author: Dennis Sullivan
Journal: Bull. Amer. Math. Soc. 6 (1982), 57-73
MSC (1980): Primary 32H20, 58F11, 58F17; Secondary 58F18, 10F05
MathSciNet review: 634434
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  • Lars V. Ahlfors, Finitely generated Kleinian groups, Amer. J. Math. 86 (1964), 413–429. MR 0167618
  • Lars V. Ahlfors, Kleinian groups, Scripta Math. 27 (1964), 97–103 (1964). MR 0171007
  • Lars V. Ahlfors, Möbius transformations in several dimensions, Ordway Professorship Lectures in Mathematics, University of Minnesota, School of Mathematics, Minneapolis, Minn., 1981. MR 725161
  • Jon Aaronson, On the pointwise ergodic behaviour of transformations preserving infinite measures, Israel J. Math. 32 (1979), no. 1, 67–82. MR 531602, 10.1007/BF02761186
  • [As] Jon Aaronson and Dennis Sullivan, Rational ergodicity of the geodesic flow on infinite volume hyperbolic manifolds (manuscript).
  • Lipman Bers, Spaces of Kleinian groups, Several Complex Variables, I (Proc. Conf., Univ. of Maryland, College Park, Md., 1970) Springer, Berlin, 1970, pp. 9–34. MR 0271333
  • Lipmann Bers, (ii) See also these proceedings.
  • [B] Rufus Bowen, Hausdorff dimension of quasi-circles, Inst. Hautes Études Sci. Publ. Math.
  • [C et al] Alain Connes, Jack Feldman and Benjamin Weiss, Amenable equivalence relations are hyperfinite, Inst. Hautes Études Sci. Publ. Math. preprint, 1980.
  • [G] Lucy Garnett, Functions and measures harmonic along the leaves of a foliation, Ph.D. Thesis, Dartmouth College, 1981; Inst. Hautes Études Sci. Publ. Math. preprint, June 1980.
  • Wolfgang Krieger, On ergodic flows and the isomorphism of factors, Math. Ann. 223 (1976), no. 1, 19–70. MR 0415341
  • [L] William LeVeque, Continued fractions for the Gaussian field, Indag. Math. (1952).
  • S. J. Patterson, The limit set of a Fuchsian group, Acta Math. 136 (1976), no. 3-4, 241–273. MR 0450547
  • Marina Ratner, Rigidity of horocycle flows, Ann. of Math. (2) 115 (1982), no. 3, 597–614. MR 657240, 10.2307/2007014
  • Dennis Sullivan, Disjoint spheres, approximation by imaginary quadratic numbers, and the logarithm law for geodesics, Acta Math. 149 (1982), no. 3-4, 215–237. MR 688349, 10.1007/BF02392354
  • Dennis 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 (State Univ. New York, Stony Brook, N.Y., 1978) Ann. of Math. Stud., vol. 97, Princeton Univ. Press, Princeton, N.J., 1981, pp. 465–496. MR 624833
  • Dennis Sullivan, The density at infinity of a discrete group of hyperbolic motions, Inst. Hautes Études Sci. Publ. Math. 50 (1979), 171–202. MR 556586
  • Dennis Sullivan, Entropy, Hausdorff measures old and new, and limit sets of geometrically finite Kleinian groups, Acta Math. 153 (1984), no. 3-4, 259–277. MR 766265, 10.1007/BF02392379
  • Dennis Sullivan, Growth of positive harmonic functions and Kleinian group limit sets of zero planar measure and Hausdorff dimension two, Geometry Symposium, Utrecht 1980 (Utrecht, 1980) Lecture Notes in Math., vol. 894, Springer, Berlin-New York, 1981, pp. 127–144. MR 655423
  • Dennis Sullivan, (vi) On the finiteness of cusps, Acta Math. (to appear).
  • Dennis Sullivan, (vii) The exponential size of a Riemannian manifold relative to heat flow, Acta Math. (submitted).
  • [Sc] Klaus Schmidt, Cocycles of ergodic group actions, Warwick Notes, 1976.
  • [T] Bill Thurston, (i) Geometry and topology of three-manifolds, preprint, Princeton Univ., 1978; to be published by Princeton Univ. Press, 1982.
  • Bill Thurston, (ii) Hyperbolic structures on 3-manifolds, I. Deformation of acylindrical manifolds, Ann. of Math. (to appear).
  • [Tu] Pekka Tukia, Rigidity of Kleinian groups and dimensionality of the limit set, preprint, Univ. of Helsinki, 1981.

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