Domains of discontinuity of Lorentzian affine group actions
We prove nonemptyness of domains of proper discontinuity of Anosov groups of affine Lorentzian transformations.
Cusp Density and Commensurability of Non-arithmetic Hyperbolic Coxeter Orbifolds
Published in Discrete & Computational Geometry
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Distribution of orbits of geometrically finite groups acting on null vectors
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...
Equidistribution of Expanding Translates of Curves in Homogeneous Spaces with the Action of (SO(n, 1)k
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...
STRUCTURAL STABILITY OF MEANDERING-HYPERBOLIC GROUP ACTIONS
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...
Crystallographic actions on Lie groups and post-Lie algebra structures
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.
Word Metric, Stationary Measure and Minkowski’s Question Mark Function
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...
A glimpse into Thurston's work
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).
On the Hirzebruch–Kobayashi–Ono proportionality principle and the non-existence of compact solvable Clifford–Klein forms...
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...
A combination theorem for Anosov subgroups
We prove an analogue of Klein combination theorem for Anosov subgroups by using a local-to-global principle for Morse quasigeodesics.
