×

Resolution of \(\overline{\partial}\) for continuable currents defined in a circular domain. (Résolution du \(\overline{\partial}\) pour les courants prolongeables définis dans un anneau.) (French) Zbl 1080.32502

Summary: We solve the \(\overline{\partial}\)-equation for extendable currents under concavity conditions on a domain \(\Omega\) of an analytic manifold. We apply these results with those of the author [Math. Nachr. 235, 179–190 (2002; Zbl 1007.32012)] to the study of the Dolbeault isomorphism on real hypersurfaces.

MSC:

32W05 \(\overline\partial\) and \(\overline\partial\)-Neumann operators
32F10 \(q\)-convexity, \(q\)-concavity
32V40 Real submanifolds in complex manifolds

Citations:

Zbl 1007.32012
PDF BibTeX XML Cite
Full Text: DOI Numdam EuDML

References:

[1] Andreotti, A., Hill, D.C., E. E. Levi convexity and the Hans Lewy Problem I, Ann. norm. super. Pisa (1972), 325-363. · Zbl 0256.32007
[2] Andreotti, A., Hill, D.C., Lojasiewicz, S. and Mackichan, B., Complexes of differential operators: the Mayer-Vietoris sequence, Inventiones Math.26 (1976), 43-86. · Zbl 0332.58016
[3] Henkin, G.M., Leiterer, J., Andreotti-Grauert theory by integrals formulas, Birkhäuser, 1986. · Zbl 0654.32002
[4] Hill, C.D., Nacinovich, M., On the Cauchy problem in complexe analysis, Annali di Matematica pura ed applicata (IV), Vol. CLXXI (1996), 159-179. · Zbl 0873.32015
[5] Hormander, L., Introduction to analysis of several complex variables, (IV edition) North-Holland company Publishing (1973). · Zbl 0271.32001
[6] Laurent-Thiébaut, CH., Phénomène de Hartogs-Bochner relatif dans une hypersurface réelle 2-concave d’une variété analytique complexe, Math. Z.212 (1993), 511-523. · Zbl 0790.32014
[7] Laurent-Thiébaut, CH., Théorie des fonctions holomorphes de plusieurs variables, Inter-Editions et CNRS Editions, 1997. · Zbl 0887.32001
[8] Laurent-Thiébaut, CH. et Leiterer, J., Andreotti- Vesentini separation theorem with Ck estimates and extension of CR forms, , 38, Princeton University (1993), 416-436. · Zbl 0776.32012
[9] Laurent-Thiébaut, CH. et Leiterer, J., Dolbeault isomorphism for CR manifolds, Prépublication de l’Institut Fourier n° 521, Grenoble (2000). · Zbl 1031.32012
[10] Lieb, I., Range, R.M., Lösungsoperatoren für den Cauchy-Riemann komplex mit Ck Abschätzungen, Math. Ann.253 (1980), 145-165. · Zbl 0441.32007
[11] Martineau, A., Distributions et valeurs au bord des fonctions holomorphes, Strasbourg RCP25 (1966).
[12] Nacinovich, M., Valli, G., Tangential Cauchy-Riemann complexes on distributions, Ann. di Matematica pura ed applicata (IV) vol. CXLVI (1987), 123-160. · Zbl 0631.58024
[13] Sambou, S., Résolution du ∂ pour les courant prolongeables, Math. Nach.235 (2002), 179-190. · Zbl 1007.32012
[14] Sambou, S., Équation de Cauchy-Riemann pour les courants prolongeables - Applications, C. R. Acad. Sci.Paris Sér. I Math., 332 (2001), 497-500. · Zbl 0992.32007
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.