Discrete conformal groups and measurable dynamics
Author:
Dennis Sullivan
Journal:
Bull. Amer. Math. Soc. 6 (1982), 5773
MSC (1980):
Primary 32H20, 58F11, 58F17; Secondary 58F18, 10F05
DOI:
https://doi.org/10.1090/S027309791982149667
MathSciNet review:
634434
Fulltext PDF
References  Similar Articles  Additional Information

[A] Lars Ahlfors, (i) Finitely generated Kleinian groups, Amer. J. Math. 86 (1964), 413429. MR 167618

Lars Ahlfors, (ii) Some remarks on Kleinian groups, Tulane Conf. Conformal mappings (1965). MR 171007
 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, https://doi.org/10.1007/BF02761186

[As] Jon Aaronson and Dennis Sullivan, Rational ergodicity of the geodesic flow on infinite volume hyperbolic manifolds (manuscript).

[B] Lipmann Bers, (i) Spaces of Kleinian groups, Several Complex Variables, I, (Maryland, 1970). MR 271333

Lipmann Bers, (ii) See also these proceedings.

[B] Rufus Bowen, Hausdorff dimension of quasicircles, 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.

[K] Wolfgang Krieger, On ergodic flows and isomorphisms of factors, Math. Ann. 223 (1976), 1970. MR 415341

[L] William LeVeque, Continued fractions for the Gaussian field, Indag. Math. (1952).

[P] S. J. Patterson, The limit set of a Fuchsian group, Acta Math. B6 (1976), 241273. [R] Dan Rudolph, manuscript (Maryland). MR 450547
 Marina Ratner, Rigidity of horocycle flows, Ann. of Math. (2) 115 (1982), no. 3, 597–614. MR 657240, https://doi.org/10.2307/2007014
 Dennis Sullivan, Disjoint spheres, approximation by imaginary quadratic numbers, and the logarithm law for geodesics, Acta Math. 149 (1982), no. 34, 215–237. MR 688349, https://doi.org/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. 34, 259–277. MR 766265, https://doi.org/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, BerlinNew 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 threemanifolds, preprint, Princeton Univ., 1978; to be published by Princeton Univ. Press, 1982.

Bill Thurston, (ii) Hyperbolic structures on 3manifolds, 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.
Retrieve articles in Bulletin of the American Mathematical Society with MSC (1980): 32H20, 58F11, 58F17, 58F18, 10F05
Retrieve articles in all journals with MSC (1980): 32H20, 58F11, 58F17, 58F18, 10F05
Additional Information
DOI:
https://doi.org/10.1090/S027309791982149667