在Schottky统一化和Jacobi参数化之间翻译辅助对称性

具有引力子和超Schottky群的形变超Riemann曲面

Deforming super Riemann surfaces with gravitinos and super Schottky groups

简要回顾了紧致（超）黎曼曲面的（超）肖特基均匀化。利用超Schottky群上同调理论，对引力子和Beltrami参数引起的超黎曼面形变进行了重新描述。它是检查的超肖特基群公式的周期矩阵的非分裂表面匹配其表达式的引力子和贝尔特拉米参数分裂表面。在附录中讨论了（超）肖特基群和通过粘合穿孔对来构造表面之间的关系。

刘维尔方程与肖特基问题

Liouville Equation And Schottky Problem

给出了紧致Riemann曲面上Poincaré度量的一个证明。这意味着，刘维方程减少到一个类似的非手征类似的更高的属关系（KP方程）中所产生的肖特基的问题解决方案的框架中的方程。这种方法将一致化（Fuchsian群）和模空间理论与KP层次相结合。除了它的数学兴趣，Angloman在二维引力中产生的量子黎曼曲面的框架中也有一些应用。

经典刘维尔作用量与轨道黎曼曲面的均匀化

Classical Liouville Action and Uniformization of Orbifold Riemann Surfaces

本文在亏格大于1的轨道黎曼曲面上研究经典刘维尔场论，通过广义肖特基空间定义正则化刘维尔作用量，证明其指数给出重言线丛张量积上的埃尔米特度量，并揭示该作用量生成辅助参数且其负值作为 Weil-Petersson 与 Takhtajan-Zograf 度量组合的 Kähler 势。

The Heisenberg Generalized Vertex Operator Algebra on a Riemann Surface

We compute the partition and correlation generating functions for the Heisenberg intertwiner generalized vertex operator algebra on a genus $g$ Riemann surface in the Schottky uniformization. These are expressed in terms of differential forms of the first, second and third kind, the prime form and the period matrix and are computed by combinatorial methods using a generalization of the MacMahon Master Theorem.

General Genus Zhu Recursion for Vertex Operator Algebras

We describe Zhu recursion for a vertex operator algebra (VOA) on a general genus Riemann surface in the Schottky uniformization where $n$-point correlation functions are written as linear combinations of $(n-1)$-point functions with universal coefficients. These coefficients are identified with specific geometric structures on the Riemann surface. We apply Zhu recursion to the Heisenberg VOA and determine all its correlation functions. For a general VOA, Zhu recursion with respect to the Virasoro vector is shown to lead to conformal Ward identities expressed in terms of derivatives with respec…

高亏格黎曼面上的全息应力张量关联函数

Holographic stress tensor correlators on higher genus Riemann surfaces

本文利用Schottky单值化技术在AdS₃/CFT₂框架下研究高亏格黎曼面上的全息应力张量关联函数，推导四点关联函数及更高点递推关系，并揭示截断AdS₃空间中T\bar{T}变形理论低点关联函数的新性质。