Proximality and equidistribution on the Furstenberg boundary

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.

References in corpus (1)

• Orbits of discrete subgroups on a symmetric space and the Furstenberg boundary