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 Γg(F):={(z,g(z)):z∈F} is complete pluripolar in CN+1. Using this result, we show that if D is an analytic polyhedron then there exists a bounded holomorphic function g such that Γg(D) is complete pluripolar in CN+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].