Equidistribution of Eisenstein series on convex co-compact hyperbolic manifolds

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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