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

Christine Laurent-Thiébaut; Egmon Porten

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 $z_{0} \in \partial Ω$ , $λ$ 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)]) : $\overline{\partial} u = λ f$ , ( $f$ is a $(0, 1)$ form, $\overline{\partial}$ closed in $U (z_{0})$ in $U (z_{0})$ with supp $(u) \subset \overline{Ω} \cap U (z_{0})$ , then we deduce an extension result for $C . R .$ functions on $\partial Ω \cap U (z_{0})$ , as holomorphic fonctions in $Ω \cap V (z_{0})$ .

An extension theorem for separately holomorphic functions with analytic singularities

Marek Jarnicki, Peter Pflug (2003)

Annales Polonici Mathematici

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Let $D_{j} \subset ℂ^{k_{j}}$ be a pseudoconvex domain and let $A_{j} \subset D_{j}$ be a locally pluriregular set, j = 1,...,N. Put $X : = ⋃_{j = 1}^{N} A ₁ \times . . . \times A_{j - 1} \times D_{j} \times A_{j + 1} \times . . . \times A_{N} \subset ℂ^{k ₁ + . . . + k_{N}}$ . 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 $ℂ^{2}$

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 $ℂ^{2}$ .

Certain partial differential subordinations on some Reinhardt domains in $ℂ^{n}$

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 $ℂ^{n}$ . 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 $f : \tilde{D} \to C^{n}$ be a holomorphic map where $\tilde{D}$ is a neighborhood of $\overline{D}$ . If $f$ is one-to-one when restricted to $b D$ , then $f : D \to f (D)$ 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 $e^{{μ ∥ z ∥}^{2}} \sum_{j = 1}^{m} {| ω_{j} |}^{2 p} < 1$ , where $(z, ω) \in ℂ^{n} \times ℂ^{m}$ . 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 $\sum_{j = 1}^{m} {| ω_{j} |}^{2 p} e^{{μ ∥ z ∥}^{2}}$ invariant.

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

A result on extension of C.R. functions

An extension theorem for separately holomorphic functions with analytic singularities

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

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

Certain partial differential subordinations on some Reinhardt domains in ℂ n

Biholomorphic maps determined on the boundary

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

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

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

Zeros of bounded holomorphic functions in strictly pseudoconvex domains in $ℂ^{2}$

Certain partial differential subordinations on some Reinhardt domains in $ℂ^{n}$