论文标题
COCOCOCTACT FUTUCHSIAN群体的基本不平等
The fundamental inequality for cocompact Fuchsian groups
论文作者
论文摘要
我们证明，对于Lebesgue量度，对于与对称双曲线多边形的相对侧面的翻译产生的任何随机行走相对于Lebesgue度量是单数的。此外，击球措施的Hausdorff维度严格少于1。 在此过程中，我们证明了CoCompact fuchsian群体的地球长度纯粹的几何不平等，并强烈让人联想到安德森 - 纳里 - 卡勒·沙伦（Anderson-Callary-Culler-Shalen）的不平等，从而在自由的克莱尼亚人群中。
We prove that the hitting measure is singular with respect to Lebesgue measure for any random walk on a cocompact Fuchsian group generated by translations joining opposite sides of a symmetric hyperbolic polygon. Moreover, the Hausdorff dimension of the hitting measure is strictly less than 1. A similar statement is proven for Coxeter groups. Along the way, we prove for cocompact Fuchsian groups a purely geometric inequality for geodesic lengths, strongly reminiscent of the Anderson-Canary-Culler-Shalen inequality for free Kleinian groups.
