Geometry of the Weil-Petersson completion of Teichmüller space

2005/02/24 by Scott A. Wolpert · 3 citations
Mathematics · #math.DG #msc:32G15

paper · pdf

published as Surveys in Differential Geometry, Vol. VIII (Boston, MA, 2002), pgs.357--393, Int. Press, Somerville, MA (2003) · 50 pages

arxiv created 2005/02/24 · arxiv updated 2009/12/01

Abstract

We present a view of the current understanding of the geometry of Weil-Petersson (WP) geodesics on the completion of the Teichmüller 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.

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• Local and Global Aspects of Weil-Petersson Geometry
• Weil-Petersson perspectives
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• The Weil-Petersson metric geometry
• Weil-Petersson geometry of Teichmuller-Coxeter complex and its finite rank property