Stein流形的解析簇上拓广的Koppelman-Leray公式  

The Extensional Koppelman-Leray Type Integral Formulas in the Analytic Varieties of Stein Manifolds

作　　者：陈叔瑾 Chen Shujin(School of Mathematical Sciences,Xiamen University,Fujian Xiamen 361005)

机构地区：[1]厦门大学数学科学学院,福建厦门361005

出　　处：《数学物理学报（A辑）》2020年第6期1492-1510,共19页Acta Mathematica Scientia

摘　　要：该文研究在Stein流形的解析簇上如何建立微分形式的积分公式.首先,使用不同的方法和技巧我们导出在Stein流形的两类有界域中对于复n-m(0≤m <n)维解析簇上微分形式的相应的积分表示式.其次,得到Stein流形的一般有界域中对于复n-m(0≤m<n)维解析簇上微分形式的统一的积分表示式.特别地,当m=0时该文所得公式正是Koppelman-Leray公式在Stein流形中的拓广.In this paper,we study how to establish integral formulas for differential forms in the analytic varieties of Stein manifolds.Firstly using different method and technique we derive the corresponding integral representation formulas of differential forms for the complex n-m(0≤m<n)dimensional analytic varieties in two types of bounded domains of Stein manifolds.Secondly we obtain the unified integral representation formulas of differential forms for the complex n-m dimensional analytic varieties in the general bounded domains of Stein manifolds,i.e.Koppelman-Leray type integral formulas for the complex n-m dimensional analytic varieties in the bounded domains of Stein manifolds.In particular,when m=0,the formulas obtained in this paper are the extension of Koppelman-Leray formula in the Stein manifolds.

关 键 词：STEIN流形 解析簇 统一公式 拓广 微分形式 积分公式 

分 类 号：O174.56[理学—数学]