Abstract
We show that the Hartogs phenomenon holds in minimal, weakly 2-pseudoconcave generic C R submanifolds of a Stein manifold with trivial normal bundle. We also prove some results concerning the local and/or global solvability of the tangential Cauchy-Riemann equations for smooth forms and currents on weakly q-pseudoconcave C R manifolds.
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References
Andreotti, A., Hill, C.D.: E.E. Levi convexity and the Hans Lewy problem I,II. Ann. Sc. Norm. Sup. Pisa 26, 325–363, 747–806 (1972)
Brinkschulte, J.: The Hartogs phenomenon in hypersurfaces with constant signature. Ann. Mat. Pura ed Appl. 183, 515–535 (2004)
Brinkschulte, J.: Local solvability of the
-equation with boundary regularity on weakly q-convex domains. Math. Ann. 334, 143–152 (2006)Brinkschulte, J.: The
-Cauchy-problem on q-convex domains. Preprint.Henkin, G. M.: The Hartogs-Bochner effect on CR manifolds. Soviet. Math. Dokl. 29, 78–82 (1984)
Henkin, G. M., Michel, V. Principe de Hartogs dans les variétés CR. J. Math. Pures Appl. 81, 1313–1395 (2002)
Hill, C.D., Nacinovich, M.: Duality and distribution cohomology of CR manifolds. Ann. Sc. Norm. Sup. Pisa 22, 315–339 (1995).
Hill, C.D., Nacinovich, M.: Pseudoconcave CR manifolds. Complex analysis and geometry (V. Ancona, E. Ballico, A. Silva, eds.), Marcel Dekker, Inc., New York, 275–297 (1996)
Hill, C.D., Nacinovich, M.: Pseudoconvexity at infinity. Selected topics in Cauchy-Riemann geometry, Quad. Mat. Dept. Math., Seconda Univ. Napoli, Caserta 9, 139–173 (2001)
Laurent-Thiébaut, C.: Résolution du
à support compact et phénomène de Hartogs-Bochner dans les variétés CR. Proc. Sympos. Pure Math. 52, 239–249 (1991)Laurent-Thiébaut, C., Leiterer, J.: Some applications of Serre duality in CR manifolds. Nagoya Math. J. 154, 141–156 (1999)
Martineau, A.: Distributions et valeurs au bord des fonctions holomorphes. RCP Strasbourg 25 (1966)
Nacinovich, M.: Poincaré lemma for tangential Cauchy-Riemann complexes. Math. Ann. 268, 449–471 (1984)
Nacinovich, M., Valli, G.: Tangential Cauchy-Riemann complexes on distributions. Ann. Mat. Pura Appl. 146, 123–160 (1987)
Porten, E.: Geometric methods in the study of CR functions and their singularities. Habilitationsschrift, Humboldt-Universität zu Berlin (2004)
Sambou, S.: Résolution du
pour les courants prolongeables. Math. Nach. 235, 179–190 (2002)
-equation with boundary regularity on weakly q-convex domains. Math. Ann. 334, 143–152 (2006)
à support compact et phénomène de Hartogs-Bochner dans les variétés CR. Proc. Sympos. Pure Math. 52, 239–249 (1991)Author information
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Brinkschulte, J. The 
-equation and the Hartogs phenomenon on weakly q-pseudoconcave C R manifolds.
manuscripta math. 120, 181–192 (2006). https://doi.org/10.1007/s00229-006-0636-z
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DOI: https://doi.org/10.1007/s00229-006-0636-z