Teichmüller disks with small limit sets in PMF

Abstract

We study limit sets of Teichmüller disks in the Thurston boundary of Teichmüller space of a closed surface S of genus at least 2. It is well known that almost every Teichmüller geodesic ray converges to a point on the boundary. We show that unlike rays, Teichmüller disks with smallest possible limit sets are extremely rare.

20 pages