论文标题
双曲线表面上的地质和矫正身份
Geodesic and orthogeodesic identities on hyperbolic surfaces
论文作者
论文摘要
双曲线表面上的大地测量长度满足有趣的方程式（称为身份），将这些长度与表面的几何量有关。本文是关于将封闭的大地地质学和矫正地理学的长度与边界长度或尖端数量相关的大家族。这些包括特殊情况，包括由于巴斯马吉人而引起的身份，麦克沙尼和米尔扎卡尼和谭旺·张。与以前的身份形成鲜明对比的是，此处介绍的身份包括所有封闭的大地测量学中的长度。
The lengths of geodesics on hyperbolic surfaces satisfy intriguing equations, known as identities, relating these lengths to geometric quantities of the surface. This paper is about a large family of identities that relate lengths of closed geodesics and orthogeodesics to boundary lengths or number of cusps. These include, as particular cases, identities due to Basmajian, to McShane and to Mirzakhani and Tan-Wong-Zhang. In stark contrast to previous identities, the identities presented here include the lengths taken among all closed geodesics.
