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Conformal measures associated to ends of hyperbolic \(n\)-manifolds. (English) Zbl 1167.30021
For a non-elementary Kleinian group with convergent Poincaré series, the authors consider certain families of open subsets of the quotient of the open unit ball with this group such that the quotient of this Kleinian group with the union of these open sets is compact. These open sets are known as the ends of this quotient surface. The authors associate to each end an \(\alpha\)-conformal measure such that the measures corresponding to different ends are mutually singular or trivial.

MSC:
30F40 Kleinian groups (aspects of compact Riemann surfaces and uniformization)
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