Complete pluripolar graphs in $ℂ^N$

• Autorzy: Nguyen Quang Dieu , Phung Van Manh
• Języki publikacji: EN

Abstrakty

EN

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].

Kategorie tematyczne

• 32U15: General pluripotential theory
• 32U30: Removable sets
• 32E20: Polynomial convexity

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2014
• Tom: 112
• Numer: 1
• Strony: 85-100

Daty

wydano

2014

Twórcy

autor

Nguyen Quang Dieu

• Hanoi National University of Education, 136 Xuan Thuy Street, Cau Giay, Hanoi, Vietnam

autor

Phung Van Manh

• Hanoi National University of Education, 136 Xuan Thuy Street, Cau Giay, Hanoi, Vietnam

Identyfikatory

DOI

10.4064/ap112-1-7