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.


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


Zbl 1007.32012
Full Text: DOI Numdam EuDML


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