发表机构
National University of Singapore; Nankai University（新加坡国立大学; 南开大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究利用Labourie–Wentworth公式与热力学形式，证明闭曲面群存在到$\u200b\mathrm{SL}_{3k}\mathbb{R}$的非Hitchin Borel Anosov表示，给出偶数维$6k$的首个例子，并分析相关局部性质。
AI 中文摘要
我们利用Labourie–Wentworth公式与热力学形式，证明在Bronstein–Davalo构造的切片上，对数最大本征值长度谱在Barbot表示附近具有一致正的二阶变分。作为主要应用，我们证明每个闭曲面群都存在到$\u200b\mathrm{SL}_{3k}\mathbb{R}$的非Hitchin Borel Anosov表示，其中$k\geqslant 1$。特别地，我们得到了偶数维$6k$中首个此类例子。我们还研究了该切片上Barbot表示附近相关对象的局部行为，包括平坦丛的Lyapunov指数、极限集的Hausdorff维数以及表示的Hilbert熵。
英文摘要
We use the Labourie--Wentworth's formula and the thermodynamic formalism to show that, along the slice constructed by Bronstein--Davalo, the logarithmic top-eigenvalue length spectrum has a uniformly positive second variation near the Barbot representation. As a major application, we show that every closed surface group admits a non-Hitchin Borel Anosov representation into $\mathrm{SL}_{3k}\mathbb{R}$ for every $k\geqslant 1$. In particular, we obtain the first such examples in the even dimensions $6k$. We also study the local behavior of related objects of this slice around the Barbot representation, including the Lyapunov exponent of the flat bundle, the Hausdorff dimension of the limit set, and the Hilbert entropy of the representation.
CommentsSeveral typos are modified. 33 pages, including an appendix and a declaration of AI use, comments are very welcome
