论文标题
随机平坦表面上的圆锥形奇点有多近？
How close are cone singularities on a random flat surface?
论文作者
论文摘要
我们研究了平锥球上最短的大地测量学，即带有圆锥形奇异性的球体上的平坦指标。两个奇数点之间最短的大地测量的长度可以视为具有规定角度缺陷的平锥球的模量空间的函数。我们证明了此函数在模量空间上的瑟斯顿体积形式的反复关系。
We study the shortest geodesics on flat cone spheres, i.e. flat metrics on the sphere with conical singularities. The length of the shortest geodesic between two singular points can be treated as a function on the moduli space of flat cone spheres with prescribed angle defects. We prove a recurrent relation on the distribution of this function with respect to Thurston's volume form on the moduli space.
