2023/02/13 by Eric Schippers, Wolfgang Staubach, Schippers, Eric +1
Mathematics · #Algebraic Geometry (math.AG) #Atomic Physics (physics.atom-ph) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2302.06408
openalex publication_date 2023/02/13 · openalex created_date 2023/02/16 · openalex updated_date 2026/07/28
Over the past two decades the theory of the Weil-Petersson metric has been extended to general Teichmüller spaces of infinite type, including for example the universal Teichmüller space. In this paper we give a survey of the main results in the Weil-Petersson geometry of infinite-dimensional Teichmüller spaces. This includes the rigorous definition of complex Hilbert manifold structures, Kähler geometry and global analysis, and generalizations of the period mapping. We also discuss the motivations of the theory in representation theory and physics beginning in the 1980s. Some examples of the appearance of Weil-Petersson Teichmüller space in other fields such as fluid mechanics and two-dimensional conformal field theory are also provided.