## Domains of discontinuity of Lorentzian affine group actions

We prove nonemptyness of domains of proper discontinuity of Anosov groups of affine Lorentzian transformations.

We prove nonemptyness of domains of proper discontinuity of Anosov groups of affine Lorentzian transformations.

Published in Discrete & Computational Geometry

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Published in Geometriae Dedicata

We study the distribution of non-discrete orbits of geometrically finite groups in SO(n,1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text {SO}}(n,1)$$\end{docume...

Published in Acta Mathematica Sinica, English Series

Let X = G/Γ be a homogeneous space with ambient group G containing the group H = (SO(n, 1))k and x ∈ X be such that Hx is dense in X. Given an analytic curve φ: I = [a, b] → H, we will show that if φ satisfies certain geometric condition, then for a typical diagonal subgroup A = {a(t): t φ ℝ}⊂ H the translates {a(t)φ(I)x: t > 0 of the curve φ(I)x w...

Abstract: In his 1985 paper, Sullivan sketched a proof of his structural stability theorem for differentiable group actions satisfying certain expansion-hyperbolicity axioms. In this paper, we relax Sullivan’s axioms and introduce a notion of meandering hyperbolicity for group actions on geodesic metric spaces. This generalization is substantial en...

Published in Communications in Mathematics

This survey on crystallographic groups, geometric structures on Lie groups and associated algebraic structures is based on a lecture given in the Ostrava research seminar in 2017.

Published in Uniform distribution theory

Given a countably infinite group G acting on some space X, an increasing family of finite subsets Gn, x∈ X and a function f over X we consider the sums Sn(f, x) = ∑g∈Gnf(gx). The asymptotic behaviour of Sn(f, x) is a delicate problem that was studied under various settings. In the following paper we study this problem when G is a specific lattice i...

We present an overview of some significant results of Thurston and their impact on mathematics. The final version of this paper will appear as Chapter 1 of the book ``In the tradition of Thurston: Geometry and topology", edited by K. Ohshika and A. Papadopoulos (Springer, 2020).

Published in Forum Mathematicum

This article continues a line of research aimed at solving an important problem of T. Kobayashi of the existence of compact Clifford–Klein forms of reductive homogeneous spaces. We contribute to this topic by showing that almost all symmetric spaces and 3-symmetric spaces do not admit solvable compact Clifford–Klein forms (with several possible exc...

We prove an analogue of Klein combination theorem for Anosov subgroups by using a local-to-global principle for Morse quasigeodesics.