EQUIDISTRIBUTION OF EISENSTEIN SERIES ON CONVEX CO-COMPACT HYPERBOLIC MANIFOLDS

For convex co-compact hyperbolic manifolds Γ\ℍn+1 for which the dimension of the limit set satisfies δΓ < 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 is the Liouville measure.