Suita conjecture and the Ohsawa-Takegoshi extension theorem

被引：1
作者：
Zbigniew Błocki
机构：
[1] Uniwersytet Jagielloński,Instytut Matematyki
来源：
Inventiones mathematicae | 2013年 / 193卷
关键词：
Recent Work; Bounded Domain; Green Function; Main Tool; Simple Proof;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We prove a conjecture of N. Suita which says that for any bounded domain D in ℂ one has \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$c_{D}^{2}\leq\pi K_{D}$\end{document}, where cD(z) is the logarithmic capacity of ℂ∖D with respect to z∈D and KD the Bergman kernel on the diagonal. We also obtain optimal constant in the Ohsawa-Takegoshi extension theorem.
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页码：149 / 158
页数：9
相关论文
共 18 条
[1]  
Berndtsson B.(1992)Weighted estimates for Duke Math. J. 66 239-255
[2]  
Berndtsson B.(1996) in domains in ℂ Ann. Inst. Fourier 46 1083-1094
[3]  
Błocki Z.(2005)The extension theorem of Ohsawa-Takegoshi and the theorem of Donnelly-Fefferman Trans. Am. Math. Soc. 357 2613-2625
[4]  
Błocki Z.(2007)The Bergman metric and the pluricomplex Green function Nagoya Math. J. 185 143-150
[5]  
Dinew Ż.(2007)Some estimates for the Bergman kernel and metric in terms of logarithmic capacity Nagoya Math. J. 188 19-30
[6]  
Dinew Ż.(2010)The Ohsawa-Takegoshi extension theorem on some unbounded sets Ann. Pol. Math. 98 147-167
[7]  
Guan Q.(2012)An example for the holomorphic sectional curvature of the Bergman metric J. Math. Pures Appl. 97 579-601
[8]  
Zhou X.(1965)On the Ohsawa-Takegoshi Acta Math. 113 89-152
[9]  
Zhu L.(1995) extension theorem and the Bochner-Kodaira identity with non-smooth twist factor Nagoya Math. J. 137 145-148
[10]  
Hörmander L.(2001) estimates and existence theorems for the Nagoya Math. J. 161 1-21
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