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Displaying similar documents to “Analytic extension from non-pseudoconvex boundaries and A ( D ) -convexity”

A result on extension of C.R. functions

Makhlouf Derridj, John Erik Fornaess (1983)

Annales de l'institut Fourier

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Let Ω an open set in C 4 near z 0 Ω , λ a suitable holomorphic function near z 0 . If we know that we can solve the following problem (see [M. Derridj, Annali. Sci. Norm. Pisa, Série IV, vol. IX (1981)]) : u = λ f , ( f is a ( 0 , 1 ) form, closed in U ( z 0 ) in U ( z 0 ) with supp ( u ) Ω U ( z 0 ) , then we deduce an extension result for C . R . functions on Ω U ( z 0 ) , as holomorphic fonctions in Ω V ( z 0 ) .

An extension theorem for separately holomorphic functions with analytic singularities

Marek Jarnicki, Peter Pflug (2003)

Annales Polonici Mathematici

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Let D j k j be a pseudoconvex domain and let A j D j be a locally pluriregular set, j = 1,...,N. Put X : = j = 1 N A × . . . × A j - 1 × D j × A j + 1 × . . . × A N k + . . . + k N . Let U be an open connected neighborhood of X and let M ⊊ U be an analytic subset. Then there exists an analytic subset M̂ of the “envelope of holomorphy” X̂ of X with M̂ ∩ X ⊂ M such that for every function f separately holomorphic on X∖M there exists an f̂ holomorphic on X̂∖M̂ with f ̂ | X M = f . The result generalizes special cases which were studied in [Ökt 1998], [Ökt 1999], [Sic 2001], and [Jar-Pfl 2001]. ...

Balls for the Kobayashi distance and extension of the automorphisms of strictly convex domains in C n with real analytic boundary

Andrea Iannuzzi (1994)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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It is shown that given a bounded strictly convex domain Ω in C n with real analitic boundary and a point x 0 in Ω , there exists a larger bounded strictly convex domain Ω with real analitic boundary, close as wished to Ω , such that Ω is a ball for the Kobayashi distance of Ω with center x 0 . The result is applied to prove that if Ω is not biholomorphic to the ball then any automorphism of Ω extends to an automorphism of Ω .

Zeros of bounded holomorphic functions in strictly pseudoconvex domains in 2

Jim Arlebrink (1993)

Annales de l'institut Fourier

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Let D be a bounded strictly pseudoconvex domain in 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 2 .

Certain partial differential subordinations on some Reinhardt domains in n

Gabriela Kohr, Mirela Kohr (1997)

Annales Polonici Mathematici

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We obtain an extension of Jack-Miller-Mocanu’s Lemma for holomorphic mappings defined in some Reinhardt domains in n . Using this result we consider first and second order partial differential subordinations for holomorphic mappings defined on the Reinhardt domain B 2 p with p ≥ 1.

Biholomorphic maps determined on the boundary

Nozomu Mochizuki (1977)

Annales de l'institut Fourier

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Let D be a bounded domain in C n such that the boundary b D is topologically S 2 n - 1 in R 2 n with a regular point; let f : D ˜ C n be a holomorphic map where D ˜ is a neighborhood of D . If f is one-to-one when restricted to b D , then f : D f ( D ) is biholomorphic.

Rigidity of the holomorphic automorphism of the generalized Fock-Bargmann-Hartogs domains

Ting Guo, Zhiming Feng, Enchao Bi (2021)

Czechoslovak Mathematical Journal

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We study a class of typical Hartogs domains which is called a generalized Fock-Bargmann-Hartogs domain D n , m p ( μ ) . The generalized Fock-Bargmann-Hartogs domain is defined by inequality e μ z 2 j = 1 m | ω j | 2 p < 1 , where ( z , ω ) n × m . In this paper, we will establish a rigidity of its holomorphic automorphism group. Our results imply that a holomorphic self-mapping of the generalized Fock-Bargmann-Hartogs domain D n , m p ( μ ) becomes a holomorphic automorphism if and only if it keeps the function j = 1 m | ω j | 2 p e μ z 2 invariant.