Graphs that are not complete pluripolar

Details Graphs that are not complete pluripolar Graphs that are not complete pluripolar

2002-03-07

arxiv.org/abs/math/0203064v1

Mathematics

Complex Variables

7 pages

Scientific paper

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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