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math.DS2022
Equidistribution of hyperbolic groups in homogeneous spaces
Ilya Gekhtman, Samuel J. Taylor, Giulio Tiozzo
We prove that infinite orbits of Zariski dense hyperbolic groups equidistribute in homogeneous spaces, in the sense that the family of measures obtained by averaging along spheres…
math.GR2022
Genericity of sublinearly Morse directions in CAT(0) spaces and the Teichmüller space
Ilya Gekhtman, Yulan Qing, Kasra Rafi
We show that the sublinearly Morse directions in the visual boundary of a rank-1 CAT(0) space with a geometric group action are generic in several commonly studied senses of the wo…