Geodesic
Plurisubharmonic Features of the TeichmÜller Metric
Publications de l'Institut Mathématique, _N_S_75 (2004) no. 89, p. 119

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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.
DOI : 10.2298/PIM0475119K
Classification : 30C62 30F45 30F60 32G15 32Q45 30C35 31A10 58B20
Keywords: quasiconformal, plurisubharmonic, Finsler metric, Teichmüller metric, Kobayashi metric, holomorphic curvature, universal Teichmüller space, Grunsky coefficients, pluricomplex Green's function 
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     title = {Plurisubharmonic {Features} of the {Teichm\"Uller} {Metric}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {119 },
     publisher = {mathdoc},
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     year = {2004},
     doi = {10.2298/PIM0475119K},
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Samuel L. Krushkal. Plurisubharmonic Features of the TeichmÜller Metric. Publications de l'Institut Mathématique, _N_S_75 (2004) no. 89, p. 119 . doi: 10.2298/PIM0475119K

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