Quasi-regular boundary and Stokes’ formula for a sub-analytic leaf. (English) Zbl 0594.32011

Pawłucki, Wiesław

Deformations, Proc. Semin., Łódź-Warsaw/Pol. 1982/84, Lect. Notes Math. 1165, 235-252 (1985).

[For the entire collection see Zbl 0568.00006.]
The author relates some differential properties of sub-analytic leaves to Whitney regularity conditions and obtains the following version of Stokes’ theorem: Let M be a p-dimensional, oriented and sub-analytic leaf in X and let \(\Sigma\) be the quasi-regular boundary of M, and \(\epsilon\) the induced 0-form on \(\Sigma\) by M. Let \(\alpha\) be a differential (p- 1)-form of class \(C^ 1\) on X, such that the set \(\bar M\cap \sup \alpha\) is compact. Then \(\int (d\alpha)_ M=\int \epsilon \alpha_{\Sigma}\).

Reviewer: K.Lancaster

MSC:

32B20	Semi-analytic sets, subanalytic sets, and generalizations
26B20	Integral formulas of real functions of several variables (Stokes, Gauss, Green, etc.)

Keywords:

quasi-regular boundary; sub-analytic leaves; Whitney regularity conditions; Stokes’ theorem

Citations:

Zbl 0568.00006