Two-dimensional slices of non-pseudoconvex open sets |
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| Authors: | Nikolai Nikolov Peter Pflug |
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| Institution: | 1. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113, Sofia, Bulgaria
2. Institut für Mathematik, Fakult?t V, Carl von Ossietzky Universit?t Oldenburg, Postfach 2503, 26111, Oldenburg, Germany
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| Abstract: | Let D be a non-pseudoconvex open set in ${\mathbb{C}^n}$ and S be the union of all two-dimensional planes with non-empty and non-pseudoconvex intersection with D. Sufficient conditions are given for ${\mathbb{C}^3{\setminus} S}$ to belong to a complex line. Moreover, in the ${{\mathcal{C}}^2}$ -smooth case, it is shown that ${S=\mathbb{C}^n}$ . |
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