Weil–Petersson Teichmüller Theory of Surfaces of Infinite Conformal Type

Eric Schippers () and Wolfgang Staubach ()
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Eric Schippers: University of Manitoba, Department of Mathematics
Wolfgang Staubach: Uppsala University, Department of Mathematics

Chapter Chapter 6 in In the Tradition of Thurston III, 2024, pp 169-247 from Springer

Abstract: Abstract 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 chapter 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.

Keywords: Teichmüller space; Quasisymmetric maps; Quasiconformal maps; Weil-Petersson; Period embedding; Complex structure; Conformal field theory; Bers embedding; Kähler potential; Kähler metric; Universal Teichmüller space; Primary: 30F60; 32G15 Secondary: 30C62; 30F30; 30F35; 58J52; 81T40 (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-43502-7_6

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DOI: 10.1007/978-3-031-43502-7_6

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