Geodesic
The Cauchy–Weil formula for differential forms
Sbornik. Mathematics, Tome 14 (1971) no. 3, pp. 383-398 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the paper one constructs and proves an analog to the Cauchy–Weil formula for differential forms on analytic polyhedra. On the way one obtains a proof for the Martinelli–Bochner formula for differential forms on domains in $\mathbf C^n$. Bibliography: 3 titles. 
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     author = {P. L. Polyakov},
     title = {The {Cauchy{\textendash}Weil} formula for differential forms},
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     volume = {14},
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P. L. Polyakov. The Cauchy–Weil formula for differential forms. Sbornik. Mathematics, Tome 14 (1971) no. 3, pp. 383-398. http://geodesic.mathdoc.fr/item/SM_1971_14_3_a4/

[1] V. A. Fuks, Vvedenie v teoriyu analiticheskikh funktsii kompleksnykh peremennykh, Fizmatgiz, Moskva, 1962

[2] W. Koppelman, “The Cauchy integral for differential forms”, Bull. Amer. Math. Soc., 73:4 (1967), 554–556 | DOI | MR | Zbl

[3] I. Lieb, Preprint, Gettingen, 1970 | MR