论文标题
圆圈表面群体作用的谐波测量和刚性
Harmonic measures and rigidity for surface group actions on the circle
论文作者
论文摘要
我们研究了$ \ operatorname {psu}（1,1）$的无扭转晶格的动作的刚度属性。我们遵循弗兰克尔（Frankel）和瑟斯顿（Thurston）在预印本中提出的方法，该方法是通过悬挂束的叉式谐波措施在预印象中提出的。我们的主要结果是曲率估计值和一个高斯 - 桥网公式，用于通过取平均值相对于谐波度量获得平均连接而获得的$ S^1 $连接。结果，我们对具有最大欧拉数的悬架叶子的谐波措施进行了精确描述，以及Matsumoto和Burger-iozzi-Wienhard的刚性定理的替代证明。
We study rigidity properties of actions of a torsion-free lattice of $\operatorname{PSU}(1,1)$ on the circle $S^1$. We follow the approaches of Frankel and Thurston proposed in preprints via foliated harmonic measures on the suspension bundles. Our main results are a curvature estimate and a Gauss--Bonnet formula for the $S^1$ connection obtained by taking the average of the flat connection with respect to a harmonic measure. As consequences, we give a precise description of the harmonic measure on suspension foliations with maximal Euler number and an alternative proof of rigidity theorems of Matsumoto and Burger--Iozzi--Wienhard.
