On the uniform equidistribution of closed horospheres in hyperbolic manifolds

Abstract

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 Strömbergsson in dimension 2. Our proofs use spectral methods, and lead to precise estimates on the rate of convergence to equidistribution.

58 pages

References in corpus (2)

• Limiting distributions of curves under geodesic flow on hyperbolic manifolds
• Asymptotic evolution of smooth curves under geodesic flow on hyperbolic manifolds - II

Cited by in corpus (1)

• On the rate of equidistribution of expanding horospheres in finite-volume quotients of $\mathrm{SL}(2,\mathbb{C})$