部分超凸曲面群表示的领引理
A collar lemma for partially hyperconvex surface group representations
摘要：
我们表明，领引理持有Anosov表示的基本群的表面到$\SL(n,\R)$，满足部分超凸性的性质，从拉布里的工作。这是几个不包含在高阶Teichmüller空间中的Anosov表示的开集的情况，以及$Θ$ -正表示为$\SO(p,q)$，如果$p\geq 4$。此外，我们表明，已知的希钦表示，如积极的ratioed和具有正特征值比的“正属性”，也持有部分超凸表示。
英文摘要：
We show that a collar lemma holds for Anosov representations of fundamental groups of surfaces into $\SL(n,\R)$ that satisfy partial hyperconvexity properties inspired from Labourie's work. This is the case for several open sets of Anosov representations not contained in higher rank Teichmüller spaces, as well as for $Θ$-positive representations into $\SO(p,q)$ if $p\geq 4$. We moreover show that 'positivity properties' known for Hitchin representations, such as being positively ratioed and having positive eigenvalue ratios, also hold for partially hyperconvex representations.
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