In this paper, we study the growth of sX(L), the number of simple closed
geodesics of length ≤ L on a complete hyperbolic surface X of finite area.
We also study the frequencies of different types of simple closed geodesics on
X and their relationship with the Weil-Petersson volumes of moduli spaces of
bordered Riemann surfaces.
This paper gives a quantitative version of Thurston’s hyperbolic Dehn surgery theorem. Applications include the ﬁrst universal bounds on the number of nonhyperbolic Dehn ﬁllings on a cusped hyperbolic 3-manifold, and estimates on the changes in volume and core geodesic length during hyperbolic Dehn ﬁlling. The proofs involve the construction of a family of hyperbolic conemanifold structures, using inﬁnitesimal harmonic deformations and analysis of geometric limits.
International Workshop on QUASICONFORMAL MAPPINGS AND THEIR APPLICATIONS
December 27, 2005 - January 01, 2006
..Indian Institute of Technology Madras Department of Mathematics
Proceedings of the International Workshop on Quasiconformal Mappings And Their Applications (IWQCMA05) December 27, 2005 - January 01, 2006
Edited by S. Ponnusamy T. Sugawa M. Vuorinen
We introduce a class of metric spaces which we call “bolic”. They include hyperbolic spaces, simply connected complete manifolds of nonpositive curvature, euclidean buildings, etc. We prove the Novikov conjecture on higher signatures for any discrete group which admits a proper isometric action on a “bolic”, weakly geodesic metric space of bounded geometry. 1. Introduction This work has grown out of an attempt to give a purely KK-theoretic proof of a result of A. Connes and H. Moscovici ([CM], [CGM]) that hyperbolic groups satisfy the Novikov conjecture. ...
Exponential decay of correlations for C 4 contact Anosov ﬂows is established. This implies, in particular, exponential decay of correlations for all smooth geodesic ﬂows in strictly negative curvature. 1. Introduction The study of decay of correlations for hyperbolic systems goes back to the work of Sinai  and Ruelle . While many results were obtained through the years for maps, some positive results have been established for Anosov ﬂows only recently.
R´sum´ anglais e e For a hyperbolic metric on a 3-dimensional manifold, the boundary of its convex core is a surface which is almost everywhere totally geodesic, but which is bent along a family of disjoint geodesics. The locus and intensity of this bending is described by a measured geodesic lamination, which is a topological object.