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Displaying similar documents to “Determination of the pluripolar hull of graphs of certain holomorphic functions”

On holomorphic maps into compact non-Kähler manifolds

Masahide Kato, Noboru Okada (2004)

Annales de l’institut Fourier

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We study the extension problem of holomorphic maps σ : H → X of a Hartogs domain H with values in a complex manifold X . For compact Kähler manifolds as well as various non-Kähler manifolds, the maximal domain Ω σ of extension for σ over Δ is contained in a subdomain of Δ . For such manifolds, we define, in this paper, an invariant Hex n ( X ) using the Hausdorff dimensions of the singular sets of σ ’s and study its properties to deduce informations on the complex structure of X .

Approximation of holomorphic functions of infinitely many variables II

László Lempert (2000)

Annales de l'institut Fourier

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Let X be a Banach space and B ( R ) ⊂ X the ball of radius R centered at 0 . Can any holomorphic function on B ( R ) be approximated by entire functions, uniformly on smaller balls B ( r ) ? We answer this question in the affirmative for a large class of Banach spaces.

A boundary cross theorem for separately holomorphic functions

Peter Pflug, Viêt-Anh Nguyên (2004)

Annales Polonici Mathematici

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Let D ⊂ ℂⁿ and G ⊂ ℂ m be pseudoconvex domains, let A (resp. B) be an open subset of the boundary ∂D (resp. ∂G) and let X be the 2-fold cross ((D∪A)×B)∪(A×(B∪G)). Suppose in addition that the domain D (resp. G) is locally ² smooth on A (resp. B). We shall determine the “envelope of holomorphy” X̂ of X in the sense that any function continuous on X and separately holomorphic on (A×G)∪(D×B) extends to a function continuous on X̂ and holomorphic on the interior of X̂. A generalization of this...

Zeros of bounded holomorphic functions in strictly pseudoconvex domains in ℂ 2

Jim Arlebrink (1993)

Annales de l'institut Fourier

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Let D be a bounded strictly pseudoconvex domain in ℂ 2 and let X be a positive divisor of D with finite area. We prove that there exists a bounded holomorphic function f such that X is the zero set of f . This result has previously been obtained by Berndtsson in the case where D is the unit ball in ℂ 2 .

Analytic extension from non-pseudoconvex boundaries and A ( D ) -convexity

Christine Laurent-Thiébaut, Egmon Porten (2003)

Annales de l’institut Fourier

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Let D ⊂ ⊂ ℂ n , n ≥ 2 , be a domain with C 2 -boundary and K ⊂ ∂ D be a compact set such that ∂ D ∖ K is connected. We study univalent analytic extension of CR-functions from ∂ D ∖ K to parts of D . Call K CR-convex if its A ( D ) -convex hull, A ( D ) - hull ( K ) , satisfies K = ∂ D ∩ A ( D ) - hull ( K ) ( A ( D ) denoting the space of functions, which are holomorphic on D and continuous up to ∂ D ). The main theorem of the paper gives analytic extension to ∂ D ∖ A ( D ) - hull ( K ) , if K is CR- convex.

A general version of the Hartogs extension theorem for separately holomorphic mappings between complex analytic spaces

Viêt-Anh Nguyên (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Using recent development in Poletsky theory of discs, we prove the following result: Let X , Y be two complex manifolds, let Z be a complex analytic space which possesses the Hartogs extension property, let A (resp. B ) be a non locally pluripolar subset of X (resp. Y ). We show that every separately holomorphic mapping f : W : = ( A × Y ) ∪ ( X × B ) → Z extends to a holomorphic mapping f ^ on W ^ : = ( z , w ) ∈ X × Y : ω ˜ ( z , A , X ) + ω ˜ ( w , B , Y ) < 1 such that f ^ = f on W ∩ W ^ , where ω ˜ ( · , A , X ) (resp. ω ˜ ( · , B , Y ) ) is the plurisubharmonic measure of A (resp. B ) relative to X (resp. Y ). Generalizations...