Counting horoballs and rational geodesics

Details Counting horoballs and rational geodesics Counting horoballs and rational geodesics

1999-12-06

arxiv.org/abs/math/9912045v2

Mathematics

Differential Geometry

7 pages,1 figure, Appendix by: K. Belabas (Orsay)

Scientific paper

Let M be a geometrically finite pinched negatively curved Riemannian manifold
with at least one cusp. We study the asymptotics of the number of geodesics in
M starting from and returning to a given cusp, and of the number of horoballs
at parabolic fixed points in the universal cover of M. In the appendix, due to
K. Belabas, the case of SL(2,Z) and of Bianchi groups is developed.

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