论文标题
虚拟同源特征值和Weil-彼得森翻译长度
Virtual homological eigenvalues and the Weil--Petersson translation length
论文作者
论文摘要
对于在可定向闭合表面上的任何伪anosov自动形态，都可以建立询问性，以确定虚拟同源特征值的某些增长与weil--petersson的翻译长度。新的询问非常适合由于小岛和麦克沙的其他知名不平等，并且由于lê。 要考虑的新数量是同源特征值的对数半径（具有多重性）的对数半径的平衡，称为同源詹森方形总和。主要定理如下。 For any cofinal sequence of regular finite covers of a given surface, together with lifts of a given pseudo-Anosov, the homological Jensen square sum of the lifts grows at most linearly fast compared to the covering degree, and the square root of the growth rate is at most $1/\sqrt{4π}$ times the Weil--Petersson translation length of the given pseudo-Anosov.
For any pseudo-Anosov automorphism on an orientable closed surface, an inquality is established bounding certain growth of virtual homological eigenvalues with the Weil--Petersson translation length. The new inquality fits nicely with other known inequalities due to Kojima and McShane, and due to Lê. The new quantity to be considered is the square sum of the logarithmic radii of the homological eigenvalues (with multiplicity) outside the complex unit circle, called the homological Jensen square sum. The main theorem is as follows. For any cofinal sequence of regular finite covers of a given surface, together with lifts of a given pseudo-Anosov, the homological Jensen square sum of the lifts grows at most linearly fast compared to the covering degree, and the square root of the growth rate is at most $1/\sqrt{4π}$ times the Weil--Petersson translation length of the given pseudo-Anosov.
