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The Green function of Teichmüller spaces with applications

Author: Samuel L. Krushkal
Journal: Bull. Amer. Math. Soc. 27 (1992), 143-147
MSC (2000): Primary 30C75; Secondary 31C10, 32G15
MathSciNet review: 1142683
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Abstract: We describe briefly a new approach to some problems related to Teichmüller spaces, invariant metrics, and extremal quasiconformal maps. This approach is based on the properties of plurisubharmonic functions, especially of the plurisubharmonic Green function.

The main theorem gives an explicit representation of the Green function for Teichmüller spaces by the Kobayashi-Teichmüller metric of these spaces. This leads to various applications. In particular, this gives a new characterization of extremal quasiconformal maps.

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