Work

Local Mixing and Invariant Measures for Horospherical Subgroups on Abelian Covers

Year: 2017

Type: article

Abstract: Abelian covers of hyperbolic three-manifolds are ubiquitous. We prove the local mixing theorem of the frame flow for abelian covers of closed hyperbolic three-manifolds. We obtain a classification theorem for measures invariant under the horospherical subgroup. We also describe applications to the prime geodesic theorem as well as to other counting and equidistribution problems. Our results are proved for any abelian cover of a homogeneous space Γ0∖G where G is a rank one simple Lie group and Γ0 < G is a convex cocompact Zariski dense subgroup.

Source: International Mathematics Research Notices

DOI: 10.1093/imrn/rnx292

Authors: Hee Oh, Wenyu Pan

Institutions: Korea Institute for Advanced Study, Yale University

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Award: Thin Groups and Dynamics