GEODESIC DISKS IN THE UNIVERSAL ASYMPTOTIC TEICHMULLER SPACE
GEODESIC DISKS IN THE UNIVERSAL ASYMPTOTIC TEICHMULLER SPACE
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通用渐近 TEICHMULLER 空间中的测地圆盘
DOI：
10.1090/tran/7541
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发表时间：
2019
影响因子：
1.3
通讯作者：
Guowu Yao
中科院分区：
文献类型：
--
作者：
Guowu Yao
设为双曲黎曼曲面。在有限维Teichmüller空间中，通过两点的测地圆盘是否唯一仍然是一个未解决的问题。在无限维的泰希米勒空间中，也不清楚有多少测地圆盘通过一个斯特列贝尔点和基点，而我们知道总是有无穷多个测地圆盘通过一个非斯特列贝尔点和基点。本文回答了在普适渐近Teichmüller空间中出现的问题，证明了总有无穷多个测地圆盘通过两点.利用渐近Teichmüller空间上的Finsler结构，得到了渐近Teichmüller度量的一个变分公式.引用
Letbe a hyperbolic Riemann surface. In a finite-dimensional Teichmüller space, it is still an open problem whether the geodesic disk passing through two points is unique. In an infinite-dimensional Teichmüller space it is also unclear how many geodesic disks pass through a Strebel point and the basepoint while we know that there are always infinitely many geodesic disks passing through a non-Strebel point and the basepoint. In this paper, we answer the problem arising in the universal asymptotic Teichmüller space and prove that there are always infinitely many geodesic disks passing through two points. Moreover, with the help of the Finsler structure on the asymptotic Teichmüller space, a variation formula for the asymptotic Teichmüller metric is obtained. References