Pluripolar hulls and fine analytic structure

Details Pluripolar hulls and fine analytic structure Pluripolar hulls and fine analytic structure

2007-09-13

arxiv.org/abs/0709.2102v2

Mathematics

Complex Variables

14 pages, revised version, to appear in Indagationes Mathematicae

Scientific paper

We discuss the relation between pluripolar hulls and fine analytic structure. Our main result is the following. For each non polar subset $S$ of the complex plane $\mathbb C$ we prove that there exists a pluripolar set $E \subset (S \times \mathbb C)$ with the property that the pluripolar hull of $E$ relative to $\mathbb C^2$ contains no fine analytic structure and its projection onto the first coordinate plane equals $\mathbb C$.

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