Distribution of orbits of geometrically finite groups acting on null vectors

2020/09/24 by Nattalie Tamam, Tamam, Nattalie, Jacqueline M. Warren +1
Mathematics · #Advanced Algebra and Geometry #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2009.11968

openalex publication_date 2020/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the distribution of non-discrete orbits of geometrically finite groups in SO(n,1) acting on ℝⁿ⁺¹, and more generally on the quotient of SO(n,1) by a horospherical subgroup. Using equidistribution of horospherical flows, we obtain both asymptotics for the distribution of orbits for the action of general geometrically finite groups, and we obtain quantitative statements with additional assumptions.

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