The Michigan Mathematical Journal

Bounds on the average bending of the convex hull boundary of a Kleinian group

Martin Bridgeman

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Michigan Math. J., Volume 51, Issue 2 (2003), 363-378.

First available in Project Euclid: 4 August 2003

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Zentralblatt MATH identifier

Primary: 51M10: Hyperbolic and elliptic geometries (general) and generalizations 52A55: Spherical and hyperbolic convexity


Bridgeman, Martin. Bounds on the average bending of the convex hull boundary of a Kleinian group. Michigan Math. J. 51 (2003), no. 2, 363--378. doi:10.1307/mmj/1060013202.

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  • A. F. Beardon, The geometry of discrete groups, Grad. Texts in Math., 91, Berlin, Springer-Verlag, 1983.
  • M. Bridgeman, Average bending of convex pleated planes in hyperbolic three-space, Invent. Math. 132 (1998), 381--391.
  • M. Bridgeman and R. D. Canary, From the boundary of the convex core to the conformal boundary, Geom. Dedicata (to appear); preprint available at $\langle $$\sim$}canary$\rangle .$
  • ------, Bounding the bending of a hyperbolic 3-manifold, preprint.
  • D. Epstein and A. Marden, Convex hulls in hyperbolic space, a theorem of Sullivan, and measured pleated surfaces, Analytical and geometric aspects of hyperbolic space (Coventry/Durham, 1984), pp. 113--253, Cambridge Univ. Press, 1987.
  • D. Epstein, A. Marden, and V. Markovic, Quasiconformal homeomorphisms and the convex hull boundary, preprint.
  • J. L. Harer and R. C. Penner, Combinatorics of train tracks, Ann. of Math. Stud., 125, Princeton Univ. Press, Princeton, NJ, 1992.
  • W. P. Thurston, The geometry and topology of 3-manifolds, lecture notes, Princeton Univ., 1979.
  • ------, Three-dimensional geometry and topology, Princeton Math. Ser., Princeton Univ. Press, Princeton, NJ, 1997.
  • ------, Minimal stretch maps between hyperbolic surfaces, preprint, $\langle $$\rangle .$