Complete pluripolar curves and graphs
Tomas Edlund
Annales Polonici Mathematici, Tome 83 (2004), p. 75-86 / Harvested from The Polish Digital Mathematics Library
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It is shown that there exist C∞ 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 Ck functions on the boundary of the unit disk. We show that this result implies that the complete pluripolar closed C∞ curves are dense in the space of closed Ck 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.

Publié le : 2004-01-01
EUDML-ID : urn:eudml:doc:280201 
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Tomas Edlund. Complete pluripolar curves and graphs. Annales Polonici Mathematici, Tome 83 (2004) pp. 75-86. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap84-1-8/