Limit sets of Weil-Petersson geodesics

Abstract

In this paper we prove that the limit set of any Weil-Petersson geodesic ray with uniquely ergodic ending lamination is a single point in the Thurston compactification of Teichmüller space. On the other hand, we construct examples of Weil-Petersson geodesics with minimal nonuniquely ergodic ending laminations and limit set a circle in the Thurston compactification.

46 pages, 3 figures, v3: some minor additions and corrections were made. The paper will appear in Int. Math. Res. Not. (IMRN)