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Proximality and equidistribution on the Furstenberg boundary

A. Gorodnik·F. Maucourant
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Abstract

Let G be a connected semisimple Lie group with finite center and without compact factors, P a minimal parabolic subgroup of G, and Γa lattice in G. We prove that every Γ-orbits in the Furstenberg boundary G/P is equidistributed for the averages over Riemannian balls. The proof is based on the proximality of the action of Γon G/P.

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A. Gorodnik, F. Maucourant. 2004-06-10. Proximality and equidistribution on the Furstenberg boundary. https://arxiv.org/abs/math/0406219

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