Exponential mixing of geodesic flows for geometrically finite hyperbolic manifolds with cusps

• 成果类型: Article
• 署名作者: Li, Jialun; Pan, Wenyu
• 署名单位: University of Zurich; University of Chicago
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-022-01156-3
• 发表日期: 2023
• 页码: 931-1021
• 关键词: closed geodesics; decay; Orbits; sets

摘要

Let Gamma be a geometrically finite discrete subgroup in SO(d + 1, 1)degrees with parabolic elements. We establish exponential mixing of the geodesic flow on the unit tangent bundle T-1 (Gamma\Hd+1) with respect to the Bowen-Margulis- Sullivan measure, which is the unique probability measure on T-1 (Gamma\Hd+1) with maximal entropy. As an application, we obtain a resonance-free region for the resolvent of the Laplacian on Gamma\Hd+1. Our approach is to construct a coding for the geodesic flow and then prove a Dolgopyat-type spectral estimate for the corresponding transfer operator.