Exponential mixing of geodesic flows for geometrically finite hyperbolic manifolds with cusps
Exponential mixing of geodesic flows for geometrically finite hyperbolic manifolds with cusps
复制标题
带尖点的几何有限双曲流形的测地流的指数混合
DOI：
10.1007/s00222-022-01156-3
复制
发表时间：
2020
影响因子：
3.1
通讯作者：
W. Pan
中科院分区：
文献类型：
--
作者：
Jialun Li;W. Pan
Let $$\Gamma $$ Γ be a geometrically finite discrete subgroup in $${\text {SO}}(d+1,1)^{\circ }$$ SO ( d + 1 , 1 ) ∘ with parabolic elements. We establish exponential mixing of the geodesic flow on the unit tangent bundle $${\text {T}}^1(\Gamma \backslash {\mathbb {H}}^{d+1})$$ T 1 ( Γ \ H d + 1 ) with respect to the Bowen–Margulis–Sullivan measure, which is the unique probability measure on $${\text {T}}^1(\Gamma \backslash {\mathbb {H}}^{d+1})$$ T 1 ( Γ \ H d + 1 ) with maximal entropy. As an application, we obtain a resonance-free region for the resolvent of the Laplacian on $$\Gamma \backslash {\mathbb {H}}^{d+1}$$ Γ \ H d + 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.
Let $$\Gamma $$ Γ be a geometrically finite discrete subgroup in $${\text {SO}}(d+1,1)^{\circ }$$ SO ( d + 1 , 1 ) ∘ with parabolic elements. We establish exponential mixing of the geodesic flow on the unit tangent bundle $${\text {T}}^1(\Gamma \backslash {\mathbb {H}}^{d+1})$$ T 1 ( Γ \ H d + 1 ) with respect to the Bowen–Margulis–Sullivan measure, which is the unique probability measure on $${\text {T}}^1(\Gamma \backslash {\mathbb {H}}^{d+1})$$ T 1 ( Γ \ H d + 1 ) with maximal entropy. As an application, we obtain a resonance-free region for the resolvent of the Laplacian on $$\Gamma \backslash {\mathbb {H}}^{d+1}$$ Γ \ H d + 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.
几何有限双曲流形上测地流的收缩目标
影响因子：
1.1
作者：
Kelmer, Dubi;Oh, Hee
通讯作者：
Oh, Hee
影响因子：
2.5
作者：
Edwards, Sam;Oh, Hee
通讯作者：
Oh, Hee