On the uniform equidistribution of closed horospheres in hyperbolic manifolds

TY - JOUR

T1 - On the uniform equidistribution of closed horospheres in hyperbolic manifolds

AU - Södergren, Carl Anders

PY - 2012/8

Y1 - 2012/8

N2 - We prove asymptotic equidistribution results for pieces of large closed horospheres in cofinite hyperbolic manifolds of arbitrary dimension. This extends earlier results by Hejhal ['On the uniform equidistribution of long closed horocycles', Loo-Keng Hua: a great mathematician of the twentieth century, Asian J. Math. 4 (2000) 839-853] and Strömbergsson ['On the uniform equidistribution of long closed horocycles', Duke Math. J. 123 (2004) 507-547] in dimension 2. Our proofs use spectral methods, and lead to precise estimates on the rate of convergence to equidistribution.

AB - We prove asymptotic equidistribution results for pieces of large closed horospheres in cofinite hyperbolic manifolds of arbitrary dimension. This extends earlier results by Hejhal ['On the uniform equidistribution of long closed horocycles', Loo-Keng Hua: a great mathematician of the twentieth century, Asian J. Math. 4 (2000) 839-853] and Strömbergsson ['On the uniform equidistribution of long closed horocycles', Duke Math. J. 123 (2004) 507-547] in dimension 2. Our proofs use spectral methods, and lead to precise estimates on the rate of convergence to equidistribution.

M3 - Journal article

SN - 0024-6115

VL - 105

SP - 225

EP - 280

JO - Proceedings of the London Mathematical Society

JF - Proceedings of the London Mathematical Society

IS - 2

ER -