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