On the lower bounds of the curvatures in a bounded domain

被引：0
|
作者：
LU Qi Keng [1 ]
机构：
[1] Institute of Mathematics, Academy of Mathematics and Systems Science,Chinese Academy of Sciences
来源：
Science China Mathematics | 2015年 / 58卷 / 01期
基金：
中国国家自然科学基金;
关键词：
minimal function; minimal integral; lower bound;
D O I：
暂无
中图分类号：
O172.2 [积分学];
学科分类号：
0701 ; 070101 ;
摘要：
Let KD(z,z)be the Bergman kernel of a bounded domain D in Cnand SectD(z,ξ)and RicciD(z,ξ)be the holomorphic sectional curvature and Ricci curvature of the Bergman metric ds2=TDαβ(z,z)dzαdzβrespectively at the point z∈D with tangent vectorξ.It is proved by constructing suitable minimal functions that SectD(z,ξ)2-2 n+2n+1 KD1(z,z)TD1αβ(z,z)ξαξβKD2(z,z)TD2λμ(z,z)ξλξμ2and RicciD(z,ξ)n+1-(n+2)KD1(z,z)TD1(z,z)ξαξβKD2(z,z)TD2λμ(z,z)ξλξμ,where z∈D1DD2,D1is a ball contained in D and D2is a ball containing D.
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页码：1 / 10
页数：10
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