Graphs that are not complete pluripolar

Armen Edigarian; Jan Wiegerinck

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Graphs that are not complete pluripolar

Armen Edigarian·Jan Wiegerinck

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Abstract

Let D_1 be a subdomain of D_2 in the complex plane CC. 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 the boundary of D_1, while the graph of f over D_1 is NOT complete pluripolar in D_2 times CC. This refutes a conjecture of Levenberg, Martin and Poletsky.

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Armen Edigarian, Jan Wiegerinck. 2002-03-07. Graphs that are not complete pluripolar. https://arxiv.org/abs/math/0203064

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