Graphs that are not complete pluripolar

Edigarian, Armen; Wiegerinck, Jan

doi:10.1090/S0002-9939-03-06947-8

Graphs that are not complete pluripolar
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by Armen Edigarian and Jan Wiegerinck

Proc. Amer. Math. Soc. 131 (2003), 2459-2465

DOI: https://doi.org/10.1090/S0002-9939-03-06947-8

Published electronically: January 8, 2003

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Abstract:

Let $D_1\subset D_2$ be domains in $\mathbb {C}$. Under very mild conditions on $D_2$ we show that there exist holomorphic functions $f$, defined on $D_1$ with the property that $f$ is nowhere extendible across $\partial D_1$, while the graph of $f$ over $D_1$ is not complete pluripolar in $D_2\times \mathbb {C}$. This refutes a conjecture of Levenberg, Martin and Poletsky (1992).

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