凸余紧双曲流形上Eisenstein级数的等分布
Equidistribution of Eisenstein series on convex co-compact hyperbolic manifolds
摘要：
对于凸余紧双曲流形$Γ\backslash \mathbb{H}^{n+1}$，当极限集的维数满足$δ_Γ< n/2$时，我们证明了与“无穷远”点$ξ$相关联的高频Eisenstein级数微局部地集中在单位余切丛中对应于以$ξ$结尾的测地线的点集所支持的测度上.这些极限测度在$ξ$中的平均值向刘维尔测度均匀分布。
英文摘要：
For convex co-compact hyperbolic manifolds $Γ\backslash \mathbb{H}^{n+1}$ for which the dimension of the limit set satisfies $δ_Γ< n/2$, we show that the high-frequency Eisenstein series associated to a point $ξ$ "at infinity" concentrate microlocally on a measure supported by (the closure of) the set of points in the unit cotangent bundle corresponding to geodesics ending at $ξ$. The average in $ξ$ of these limit measures equidistributes towards the Liouville measure.
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