带尖点的Hitchin表示的熵刚性

带正性的尖点 Borel Anosov 表示

Cusped Borel Anosov representations with positivity

本文研究带正性的尖点 Borel Anosov 表示，证明像中含单 Jordan 块幂幺元时必为尖点 Hitchin 表示，并指出其与非 Hitchin 表示的融合不再保持尖点 Borel Anosov 性质。

Cusped Hitchin representations and Anosov representations of geometrically finite Fuchsian groups

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 establish analogues of many properties of traditional Anosov representations. In particular, we show that our Anosov representations are stable under type-preserving deformations and that their limit maps vary analytically. We also observe that our Anosov representations fit into the previous frameworks of relatively Anosov and relatively dominated representations developed by Kapovich-Leeb and Zhu.

有限扩张刚性通过带凹口的双曲3流形的Dehn填充 witnessed

Profinite rigidity witnessed by Dehn fillings of cusped hyperbolic 3-manifolds

本文通过研究带凹口的双曲3流形的Dehn填充，证明了某些流形在所有紧致定向3流形中是有限扩张刚性的，并改进了双曲结或双曲型卫星结的有限扩张刚性判据。

Hitchin流形中测地平面的分形闭包

Fractal closures of geodesic planes in Hitchin manifolds

该研究通过构造 Hitchin 流形中的漂浮测地平面，证明了其闭包为分形，揭示了高秩无限体积情况下非紧类型局部对称空间的拓扑刚性反例。

On entropy, regularity and rigidity for convex representations of hyperbolic manifolds

Given a convex representation $ρ:Γ\to\textrm{PGL}(d,\mathbb{R})$ of a convex co-compact group $Γ$ of $\mathbb{H}^k$ we find upper bounds for the quantity $αh_ρ,$ where $h_ρ$ is the entropy of $ρ$ and $α$ is the Hölder exponent of the equivariant map $\partialΓ\to\mathbb{P}(\mathbb{R}^d).$ We also give rigidity statements when the upper bound is attained. We then study Hitchin representations and prove that if $ρ:π_1Σ\to\textrm{PSL}(d,\mathbb{R})$ is in the Hitchin component then $αh_ρ\leq 2/(d-1)$ (where $α$ is the Hölder exponent of the map $ζ:\partial\mathbb{H}^2\to\mathscr{F}$) with equalit…

通过自连接实现表示的共形测度刚性

Conformal measure rigidity for representations via self-joinings

本文利用自连接群的高秩共形测度研究离散忠实表示的刚性，证明在发散型或 Anosov 表示情形下，边界映射前推的共形测度类可判定表示的可延展性，并推广了 Sullivan、Tukia、Yue 的刚性定理。