Inventiones mathematicae

, Volume 146, Issue 1, pp 143–192

Bounded geometry for Kleinian groups

  • Yair N. Minsky

DOI: 10.1007/s002220100163

Cite this article as:
Minsky, Y. Invent. math. (2001) 146: 143. doi:10.1007/s002220100163


We show that a Kleinian surface group, or hyperbolic 3-manifold with a cusp-preserving homotopy-equivalence to a surface, has bounded geometry if and only if there is an upper bound on an associated collection of coefficients that depend only on its end invariants. Bounded geometry is a positive lower bound on the lengths of closed geodesics. When the surface is a once-punctured torus, the coefficients coincide with the continued fraction coefficients associated to the ending laminations.

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Yair N. Minsky
    • 1
  1. 1.SUNY at Stony Brook, Institute for Mathematical Sciences, Stony Brook, NY 11794-3651, USAUSA

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