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Creators/Authors contains: "Zhang, Tengren"

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  1. ; ; (, Mathematische Annalen)
    Free, publicly-accessible full text available June 1, 2026
  2. ; ; (, Journal of Modern Dynamics)
    Forni, Giovanni (Ed.)
    We study Patterson–Sullivan measures for a class of discrete subgroups of higher rank semisimple Lie groups, called transverse groups, whose limit set is well-defined and transverse in a partial flag variety. This class of groups includes both Anosov and relatively Anosov groups, as well as all discrete subgroups of rank one Lie groups. We prove an analogue of the Hopf–Tsuji–Sullivan dichotomy and then use this dichotomy to prove a variant of Burger's Manhattan Curve Theorem. We also use the Patterson–Sullivan measures to obtain conditions for when a subgroup has critical exponent strictly less than the original transverse group. These gap results are new even for Anosov groups. 
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  3. ; ; (, Advances in Mathematics)
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  4. ; (, Geometric and Functional Analysis)
    Properly discontinuous actions of a surface group by affine automorphisms of ℝ^d were shown to exist by Danciger-Gueritaud-Kassel. We show, however, that if the linear part of an affine surface group action is in the Hitchin component, then the action fails to be properly discontinuous. The key case is that of linear part in 𝖲𝖮(n,n−1), so that the affine action is by isometries of a flat pseudo-Riemannian metric on ℝ^d of signature (n,n−1). Here, the translational part determines a deformation of the linear part into 𝖯𝖲𝖮(n,n)-Hitchin representations and the crucial step is to show that such representations are not Anosov in 𝖯𝖲𝖫(2n,ℝ) with respect to the stabilizer of an n-plane. We also prove a negative curvature analogue of the main result, that the action of a surface group on the pseudo-Riemannian hyperbolic space of signature (n,n−1) by a 𝖯𝖲𝖮(n,n)-Hitchin representation fails to be properly discontinuous. 
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