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• W2540726712 abstract "Let U be a pseudoconvex open set in a complex manifold M. When is U a Stein manifold? There are classical counter examples due to Grauert, even when U has real-analytic boundary or has strictly pseudoconvex points. We give new criteria for the Steinness of U and we analyze the obstructions. The main tool is the notion of Levi-currents. They are positive $${partial overline{partial }}$$ -closed currents T of bidimension (1, 1) and of mass 1 directed by the directions where all continuous psh functions in U have vanishing Levi-form. The extremal ones, are supported on the sets where all continuous psh functions are constant. We also construct under geometric conditions, bounded strictly psh exhaustion functions, and hence we obtain Donnelly–Fefferman weights. To any infinitesimally homogeneous manifold, we associate a foliation. The dynamics of the foliation determines the solution of the Levi-problem. Some of the results can be extended to the context of pseudoconvexity with respect to a Pfaff-system." @default.
• W2540726712 created "2016-11-04" @default.
• W2540726712 creator A5065874352 @default.
• W2540726712 date "2017-04-06" @default.
• W2540726712 modified "2023-10-14" @default.
• W2540726712 title "Levi problem in complex manifolds" @default.
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• W2540726712 doi "https://doi.org/10.1007/s00208-017-1539-x" @default.
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