2015/06/29 by Guowu Yao, Yao, Guowu
Mathematics · #30C62 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Geometric and Algebraic Topology #Primary 30C75 #math.CV #msc:30C62 #msc:30C75
paper · pdf · doi:10.48550/arxiv.1506.08816
19 pages. arXiv admin note: substantial text overlap with arXiv:1506.08769
arxiv created 2015/06/29 · openalex publication_date 2015/06/29 · arxiv updated 2015/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let S be a hyperbolic Riemann surface. In a finite-dimensional Teichmüller space T(S), 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 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.