Geodesic disks in asymptotic Teichmüller space

Abstract

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.

19 pages. arXiv admin note: substantial text overlap with arXiv:1506.08769