Graphs that are not complete pluripolar

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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.
7 pages

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Complex Variables, 32U30; 31A15

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http://salesiana.dossiersoluciones.com/handle/123456789/63510

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0203064
 http://arxiv.org/abs/math/0203064

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arXiv