PUBLICATIONS DE L'INSTITUT MATHEMATIQUE (BEOGRAD) (N.S.)Vol. 75(89), pp. 119–138 (2004)
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PUBLICATIONS DE L'INSTITUT MATHEMATIQUE (BEOGRAD) (N.S.) Vol. 75(89), pp. 119–138 (2004) |
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PLURISUBHARMONIC FEATURES OF THE TEICHMÜLLER METRICSamuel L. KrushkalResearch Institute for Mathematical Sciences, Department of Mathematics and Statistics, Bar-Ilan University, 52900 Ramat-Gan, IsraelAbstract: The key result of this paper is a strengthened version for universal Teichmüller space of the fundamental Gardiner–Royden theorem on coincidence of the Kobayashi and Teichmüller metrics for Teichmüller spaces. Using the Grunsky coefficient inequalities for univalent functions, we show that the Teichmüller metric is logarithmically plurisubharmonic and has constant holomorphic sectional curvature $\kappa_{\mathcal K}(\psi,v)=-4$. This result has various important applications in geometric function theory and geometry. Some applications to complex geometry of Teichmüller spaces are given. Keywords: Quasiconformal, plurisubharmonic, Finsler metric, Teichmüller metric, Kobayashi metric, holomorphic curvature, universal Teichmüller space, Grunsky coefficients, pluricomplex Green's function Classification (MSC2000): 30C62, 30F45, 30F60, 32G15, 32Q45; 30C35, 31A10, 58B20 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 27 Oct 2004. This page was last modified: 22 Feb 2005.
© 2004 Mathematical Institute of the Serbian Academy of Science and Arts
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