Complete pluripolar graphs in ${ℂ}^N$

Nguyen Quang Dieu, and Phung Van Manh. "Complete pluripolar graphs in $ℂ^N$." Annales Polonici Mathematici 112.1 (2014): 85-100. <http://eudml.org/doc/280999>.

@article{NguyenQuangDieu2014,
abstract = {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 $Γ_g(F):=\{(z, g(z)): z ∈ F\}$ is complete pluripolar in $ℂ^\{N+1\}$. Using this result, we show that if D is an analytic polyhedron then there exists a bounded holomorphic function g such that $Γ_g(D)$ is complete pluripolar in $ℂ^\{N+1\}$. 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].},
author = {Nguyen Quang Dieu, Phung Van Manh},
journal = {Annales Polonici Mathematici},
keywords = {complete pluripolar set; pluripolar hull},
language = {eng},
number = {1},
pages = {85-100},
title = {Complete pluripolar graphs in $ℂ^N$},
url = {http://eudml.org/doc/280999},
volume = {112},
year = {2014},
}

TY - JOUR
AU - Nguyen Quang Dieu
AU - Phung Van Manh
TI - Complete pluripolar graphs in $ℂ^N$
JO - Annales Polonici Mathematici
PY - 2014
VL - 112
IS - 1
SP - 85
EP - 100
AB - 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 $Γ_g(F):={(z, g(z)): z ∈ F}$ is complete pluripolar in $ℂ^{N+1}$. Using this result, we show that if D is an analytic polyhedron then there exists a bounded holomorphic function g such that $Γ_g(D)$ is complete pluripolar in $ℂ^{N+1}$. 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].
LA - eng
KW - complete pluripolar set; pluripolar hull
UR - http://eudml.org/doc/280999
ER -