On the uniform equidistribution of closed horospheres in hyperbolic manifolds

Details On the uniform equidistribution of closed horospheres in hyperbolic manifolds On the uniform equidistribution of closed horospheres in hyperbolic manifolds

2011-03-17

arxiv.org/abs/1103.3444v1

Mathematics

Dynamical Systems

58 pages

Scientific paper

We prove asymptotic equidistribution results for pieces of large closed
horospheres in cofinite hyperbolic manifolds of arbitrary dimension. This
extends earlier results by Hejhal and Str\"ombergsson in dimension 2. Our
proofs use spectral methods, and lead to precise estimates on the rate of
convergence to equidistribution.

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