An avoidance principle and Margulis functions for expanding translates of unipotent orbits

2022/06/24 by Anthony Sanchez, Sanchez, Anthony, Juno Seong +1 · 1 citation
Mathematics · #22E46 (Secondary) #22F30 (Primary) 37D40 #Advanced Algebra and Geometry #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2206.12019

openalex publication_date 2022/06/24 · openalex created_date 2022/06/29 · openalex updated_date 2026/07/28

Abstract

We prove an avoidance principle for expanding translates of unipotent orbits for some semisimple homogeneous spaces. In addition, we prove a quantitative isolation result of closed orbits and give an upper bound on the number of closed orbits of bounded volume. The proofs of our results rely on the construction of a Margulis function and the theory of finite dimensional representations of semisimple Lie groups.

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