Weil-Petersson geometry of Teichmuller-Coxeter complex and its finite rank property

2008/05/18 by Yamada, Sumio
#30F60 (Primary) #51F15 #53C21 (Secondary) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0805.2762

Abstract

We construct a Weil-Petersson geodesic completion of Teichmuller space through the formalism of Coxeter complex with the Teichmuller space as its non-linear non-homogeneous fundamental domain. We show that the metric and geodesic completions both satisfy a finite rank property, demonstrating a similarity with the non-compact symmetric spaces of semi-simple Lie groups.

Related

• Geometry of the Weil-Petersson completion of Teichmüller space
• Weil-Petersson perspectives
• Local and Global Aspects of Weil-Petersson Geometry
• Weil-Petersson Teichmüller theory of surfaces of infinite conformal type
• Classification of Weil-Petersson Isometries