18 citations · 68 across the 18 of their papers we have counts for
19 papers
Geometric finiteness in paracomplex hyperbolic spaces
Tianqi Wang, Zhufeng Yao, Tengren Zhang
We develop a framework for studying discrete subgroups of via the paracomplex hyperbolic space , a rank- pseudo-Riemannian symmetr…
Orbital counting for relatively Anosov groups
Richard Canary, Tengren Zhang, Feng Zhu +1
We obtain orbital counting results for relatively Anosov groups with respect to linear functionals with finite critical exponent. Our counting results follow from an equidistributi…
Patterson-Sullivan measures for relatively Anosov groups
Richard Canary, Andrew Zimmer, Tengren Zhang
We establish existence, uniqueness and ergodicity results for Patterson-Sullivan measures for relatively Anosov groups. As applications we obtain an entropy gap theorem and a stric…
Cusped Borel Anosov representations with positivity
Tengren Zhang, Gye-Seon Lee
We show that if a cusped Borel Anosov representation from a lattice to contains a unipotent element with a single…
-pleated surfaces and their shear-bend coordinates
Sara Maloni, Giuseppe Martone, Filippo Mazzoli +1
In this article, we single out representations of surface groups into which generalize the well-studied family of pleated surfaces into $\mathsf{PSL}_2…
Patterson-Sullivan measures for transverse subgroups
Richard Canary, Tengren Zhang, Andrew Zimmer
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 transvers…
Entropy rigidity for cusped Hitchin representations
Richard Canary, Tengren Zhang, Andrew Zimmer
We establish an entropy rigidity theorem for Hitchin representations of all geometrically finite Fuchsian groups which generalizes a theorem of Potrie and Sambarino for Hitchin rep…
Cusped Hitchin representations and Anosov representations of geometrically finite Fuchsian groups
Richard Canary, Tengren Zhang, Andrew Zimmer
We develop a theory of Anosov representation of geometrically finite Fuchsian groups in SL(d,R) and show that cusped Hitchin representations are Borel Anosov in this sense. We esta…
Weakly positive and directed Anosov representations
Sungwoon Kim, Ser Peow Tan, Tengren Zhang
Given a finitely generated group , a directed graph , and a map , we introduce the notion of an -directed Anosov representation. This is a weakening of the no…
Regularity of limit sets of Anosov representations
Tengren Zhang, Andrew Zimmer
In this paper we establish necessary and sufficient conditions for the limit set of a projective Anosov representation to be a differentiable submanifold of projective space with H…
Affine actions with Hitchin linear part
Jeffrey Danciger, Tengren Zhang
Properly discontinuous actions of a surface group by affine automorphisms of were shown to exist by Danciger-Gueritaud-Kassel. We show, however, that if the linear pa…
Coordinates on the augmented moduli space of convex RP^2 structures
John Loftin, Tengren Zhang
Let S be an orientable, finite type surface with negative Euler characteristic. The augmented moduli space of convex real projective structures on S was first defined and topologiz…
The Goldman symplectic form on the PGL(V)-Hitchin component
Zhe Sun, Tengren Zhang
This article is the second of a pair of articles about the Goldman symplectic form on the PGL(V)-Hitchin component of a closed, connected, oriented, hyperbolic surface S. We show t…
Flows on the PGL(V)-Hitchin component
Zhe Sun, Anna Wienhard, Tengren Zhang
In this article we define new flows on the Hitchin components for PGL(V). Special examples of these flows are associated to simple closed curves on the surface and give generalized…
Deforming convex real projective structures
Anna Wienhard, Tengren Zhang
Let S be a closed, connected, orientable surface of genus at least 2, and let C(S) denote the deformation space of convex real projective structures S. In this article, we introduc…
Positively ratioed representations
Giuseppe Martone, Tengren Zhang
Let S be a closed orientable surface of genus at least 2 and let G be a semisimple real algebraic group of non-compact type. We consider a class of representations from the fundame…
Collar lemma for Hitchin representations
Gye-Seon Lee, Tengren Zhang
In this article, we prove an analog of the classical collar lemma in the setting of Hitchin representations.
Degeneration of Hitchin representations along internal sequences
Tengren Zhang
Using the work of Bonahon-Dreyer and Fock-Goncharov, one can construct a real-analytic parameterization for the PSL(n,R) Hitchin component of a surface S, that is explicitly analog…
The degeneration of convex RP^2 structures on surfaces
Tengren Zhang
Let M be a compact surface of negative Euler characteristic and let C(M) be the deformation space of convex real projective structures on M. For every choice of pants decomposition…