数学物理学报 ›› 2020, Vol. 40 ›› Issue (6): 1492-1510.

• 论文 • 上一篇    下一篇

Stein流形的解析簇上拓广的Koppelman-Leray公式

陈叔瑾*()   

  1. 厦门大学数学科学学院 福建厦门 361005
  • 收稿日期:2018-08-15 出版日期:2020-12-26 发布日期:2020-12-29
  • 通讯作者: 陈叔瑾 E-mail:shjchen39@163.com

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

Shujin Chen*()   

  1. School of Mathematical Sciences, Xiamen University, Fujian Xiamen 361005
  • Received:2018-08-15 Online:2020-12-26 Published:2020-12-29
  • Contact: Shujin Chen E-mail:shjchen39@163.com

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.

关键词: Stein流形, 解析簇, 统一公式, 拓广, 微分形式, 积分公式

Abstract:

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.

Key words: Stein manifold, Analytic varieties, Unified formula, Extension, Differential form, Integral formula

中图分类号: 

  • O174.56