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Complete pluripolar graphs in N

Nguyen Quang Dieu, Phung Van Manh (2014)

Annales Polonici Mathematici

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 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 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]...

Cousin-I spaces and domains of holomorphy

Ilie Bârză, Viorel Vâjâitu (2009)

Annales Polonici Mathematici

We prove that a Cousin-I open set D of an irreducible projective surface X is locally Stein at every boundary point which lies in X r e g . In particular, Cousin-I proper open sets of ℙ² are Stein. We also study K-envelopes of holomorphy of K-complete spaces.

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