Dynamical properties of the Weil-Petersson metric

2009/01/27 by Hamenstadt, Ursula
#20F67 #30F60 #37D40 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.0901.4301

Abstract

Let S be a non-exceptional oriented surface of finite type. We discuss the action of subgroups of the mapping class group of S on the CAT(0)-boundary of the completion of Teichmueller space with respect to the Weil-Petersson metric. We show that the set of invariant Borel probability measures for the Weil-Petersson flow on moduli space which are supported on closed orbits is dense in the space of invariant Borel probability measures.

Related

• Teichmueller flow and Weil-Petersson flow
• The geometry of the Weil-Petersson metric in complex dynamics
• Lecture notes on the dynamics of the Weil-Petersson flow
• Weil-Petersson Completion of Teichmueller Spaces and Mapping Class Group Actions
• Classification of Weil-Petersson Isometries