Let F be the Cartesian product of N closed sets in ℂ. We prove that there exists a function g which is continuous on F and holomorphic on the interior of F such that is complete pluripolar in . Using this result, we show that if D is an analytic polyhedron then there exists a bounded holomorphic function g such that is complete pluripolar in . These results are high-dimensional analogs of the previous ones due to Edlund [Complete pluripolar curves and graphs, Ann. Polon. Math. 84 (2004), 75-86] and Levenberg, Martin and Poletsky [Analytic disks and pluripolar sets, Indiana Univ. Math. J. 41 (1992), 515-532].
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap112-1-7,
author = {Nguyen Quang Dieu and Phung Van Manh},
title = {Complete pluripolar graphs in $$\mathbb{C}$^N$
},
journal = {Annales Polonici Mathematici},
volume = {111},
year = {2014},
pages = {85-100},
zbl = {1329.32019},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap112-1-7}
}
Nguyen Quang Dieu; Phung Van Manh. Complete pluripolar graphs in $ℂ^N$
. Annales Polonici Mathematici, Tome 111 (2014) pp. 85-100. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap112-1-7/