20 citations · 33 across the 11 of their papers we have counts for
11 papers
Correlation Number for Potentials with Entropy Gaps and Cusped Hitchin Representations
Lien-Yung Kao, Giuseppe Martone
We introduce a correlation number for two strictly positive, locally Hölder continuous, independent potentials with strong entropy gaps at infinity on a topologically mixing counta…
Pressure gaps, geometric potentials, and nonpositively curved manifolds
Dong Chen, Lien-Yung Kao, Kiho Park
In this paper, we derive a general pressure gap criterion for closed rank 1 manifolds whose singular sets are given by codimension 1 totally geodesic flat subtori. As an applicatio…
Pressure metrics for cusped Hitchin components
Harrison Bray, Richard Canary, Lien-Yung Kao +1
We study the cusped Hitchin component consisting of (conjugacy classes of) cusped Hitchin representations of a torsion-free geometrically finite Fuchsian group into PSL(d,R). We pr…
Counting, equidistribution and entropy gaps at infinity with applications to cusped Hitchin representations
Harrison Bray, Richard Canary, Lien-Yung Kao +1
We show that if an eventually positive, non-arithmetic, locally Hölder continuous potential for a topologically mixing countable Markov shift with (BIP) has an entropy gap at infin…
Pressure metrics for deformation spaces of quasifuchsian groups with parabolics
Harrison Bray, Richard Canary, Lien-Yung Kao
In this paper, we produce a mapping class group invariant pressure metric on the space QF(S) of quasiconformal deformations of a co-finite area Fuchsian group uniformizing a surfac…
Properties of equilibrium states for geodesic flows over manifolds without focal points
Dong Chen, Lien-Yung Kao, Kiho Park
We prove that for closed rank 1 manifolds without focal points the equilibrium states are unique for Hölder potentials satisfying the pressure gap condition. In addition, we provid…
Pressure metrics and Manhattan curves for Teichmüller spaces of punctured surfaces
Lien-Yung Kao
In this paper, we extend the construction of pressure metrics to Teichmüller spaces of surfaces with punctures. This construction recovers Thurston's Riemannian metric on Teichmüll…
Unique equilibrium states for geodesic flows over surfaces without focal points
Dong Chen, Lien-Yung Kao, Kiho Park
In this paper, we study dynamics of geodesic flows over closed surfaces of genus greater than or equal to 2 without focal points. Especially, we prove that there is a large class o…
Manhattan Curves for Hyperbolic Surfaces with Cusps
Lien-Yung Kao
In this paper, we study an interesting curve, so-called the Manhattan curve, associated with a pair of boundary-preserving Fuchsian representations of a (non-compact) surface, espe…
Pressure type metrics on spaces of metric graphs
Lien-Yung Kao
In this note, we consider two Riemannian metrics on a moduli space of metric graphs. Each of them could be thought of as an analogue of the Weil-Petersson metric on the moduli spac…
Entropy, Critical Exponent and Immersed Surfaces in Hyperbolic 3-Manifolds
Lien-Yung Kao
We consider a --injective immersion from a compact surface to a hyperbolic 3--manifold . Let denote the copy of in $\mathrm{Isom}({\mathbb{H}}…