论文标题
Weil-petersson体积多项式的高造物渐近扩张
A high-genus asymptotic expansion of Weil-Petersson volume polynomials
论文作者
论文摘要
本文中所考虑的对象是总卷$ v_ {g，n}（x_1，\ ldots，x_n）$的$ g $的双曲线表面的$ g $的$ n $边界组件的长度为$ x_1，\ ldots，x_n $，x_n $，x_n $，用于Weil-Petersson卷。我们证明了数量$ v_ {g，n}（x_1，\ ldots，x_n）$的渐近扩展在该属$ g $的负功率方面，对固定$ n $和任何$ x_1，\ ldots，x_n \ geq 0 $ th。这一扩展的第一个任期出现在Mirzakhani和Petri（2019）的工作中，我们明确地计算了第二个任期。证明中使用的主要工具是Mirzakhani的拓扑递归公式，我们为此提供了全面的介绍。
The object under consideration in this article is the total volume $V_{g,n}(x_1, \ldots, x_n)$ of the moduli space of hyperbolic surfaces of genus $g$ with $n$ boundary components of lengths $x_1, \ldots, x_n$, for the Weil-Petersson volume form. We prove the existence of an asymptotic expansion of the quantity $V_{g,n}(x_1, \ldots, x_n)$ in terms of negative powers of the genus $g$, true for fixed $n$ and any $x_1, \ldots, x_n \geq 0$. The first term of this expansion appears in work of Mirzakhani and Petri (2019), and we compute the second term explicitly. The main tool used in the proof is Mirzakhani's topological recursion formula, for which we provide a comprehensive introduction.
