Complete pluripolar curves and graphs
It is shown that there exist functions on the boundary of the unit disk whose graphs are complete pluripolar. Moreover, for any natural number k, such functions are dense in the space of functions on the boundary of the unit disk. We show that this result implies that the complete pluripolar closed curves are dense in the space of closed curves in ℂⁿ. We also show that on each closed subset of the complex plane there is a continuous function whose graph is complete pluripolar.