Graphs that are not complete pluripolar
Armen Edigarian, Jan Wiegerinck
Abstract
Let D1 be a subdomain of D2 in the complex plane CC. Under very mild conditions on D2 we show that there exist holomorphic functions f, defined on D1 with the property that f is nowhere extendible across the boundary of D1, while the graph of f over D1 is NOT complete pluripolar in D2 times CC. This refutes a conjecture of Levenberg, Martin and Poletsky.
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