Geometry of the Weil-Peterson completion of Teichmüller space

Abstract

We present a view of the current understanding of the geometry of Weil-Petersson (WP) geodesics on the completion of the Teichm"uller space. We sketch a collection of results by other authors and then proceed to develop the properties of the WP CAT(0) geometry. Our approach includes a simplified proof of the Masur-Wolf theorem, a classification of flats and of geodesic limits.