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

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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
@article{10_2298_PIM0475119K,
     author = {Samuel L. Krushkal},
     title = {Plurisubharmonic {Features} of the {Teichm\"Uller} {Metric}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {119 },
     publisher = {mathdoc},
     volume = {_N_S_75},
     number = {89},
     year = {2004},
     doi = {10.2298/PIM0475119K},
     zbl = {1079.30019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/PIM0475119K/}
}
TY  - JOUR
AU  - Samuel L. Krushkal
TI  - Plurisubharmonic Features of the TeichmÜller Metric
JO  - Publications de l'Institut Mathématique
PY  - 2004
SP  - 119 
VL  - _N_S_75
IS  - 89
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.2298/PIM0475119K/
DO  - 10.2298/PIM0475119K
LA  - en
ID  - 10_2298_PIM0475119K
ER  - 
%0 Journal Article
%A Samuel L. Krushkal
%T Plurisubharmonic Features of the TeichmÜller Metric
%J Publications de l'Institut Mathématique
%D 2004
%P 119 
%V _N_S_75
%N 89
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.2298/PIM0475119K/
%R 10.2298/PIM0475119K
%G en
%F 10_2298_PIM0475119K
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. http://geodesic.mathdoc.fr/articles/10.2298/PIM0475119K/

Cité par Sources :