论文标题
二分法和阿诺索夫组极限集的措施
Dichotomy and measures on limit sets of Anosov groups
论文作者
论文摘要
令$ g $为连接的半神经真实代数集团。对于任何Zariski密集的Anosov子组$γ<g $，我们表明，当$γ$ - 符合的度量在$γ$的限制集中支持，并且仅当其“尺寸”为$γ$ - 临界。这意味着每个临界维度的$γ$ - 符合措施的独特性。我们从Hopf-Tsuji-Sullivan二分法的较高等级类似物中推断出来，以实现最大对角线作用。其他应用程序包括AHLFOR的类似物测量Anosov子组的猜想。
Let $G$ be a connected semisimple real algebraic group. For any Zariski dense Anosov subgroup $Γ<G$, we show that a $Γ$-conformal measure is supported on the limit set of $Γ$ if and only if its "dimension" is $Γ$-critical. This implies the uniqueness of a $Γ$-conformal measure for each critical dimension. We deduce this from a higher rank analogue of the Hopf-Tsuji-Sullivan dichotomy for the maximal diagonal action. Other applications include an analogue of the Ahlfors measure conjecture for Anosov subgroups.
