Two-dimensional slices of non-pseudoconvex open sets

Details Two-dimensional slices of non-pseudoconvex open sets Two-dimensional slices of non-pseudoconvex open sets

2011-03-22

arxiv.org/abs/1103.4323v1

Mathematics

Complex Variables

Scientific paper

Let $D$ be a non-pseudoconvex open set in $\C^3$ and $S$ be the union of all
two-dimensional planes with non-empty and non-pseudoconvex intersection with
$D.$ Sufficient conditions are given for $\C^3\setminus S$ to belong to a
complex line. Moreover, in the $\mathcal C^2$-smooth case, it is shown that
$S=\C^n$.

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