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Pseudoconvex domains are exhausted in such a way that we keep a part of the boundary fixed in all the domains of the exhaustion. This is used to solve a problem concerning whether the generators for the ideal of either the holomorphic functions continuous up to the boundary or the bounded holomorphic functions, vanishing at a point in $ℂ^{n}$ where the fibre is nontrivial, has to exceed $n$ . This is shown not to be the case.

Triviality of scalar linear type isotropy subgroup by passing to an alternative canonical form of a hypersurface

Vladimir V. Ežov (1998)

Annales Polonici Mathematici

The Chern-Moser (CM) normal form of a real hypersurface in $ℂ^{N}$ can be obtained by considering automorphisms whose derivative acts as the identity on the complex tangent space. However, the CM normal form is also invariant under a larger group (pseudo-unitary linear transformations) and it is this property that makes the CM normal form special. Without this additional restriction, various types of normal forms occur. One of them helps to give a simple proof of a (previously complicated) theorem about...

Truncated microsupport and holomorphic solutions of D-modules

Masaki Kashiwara, Teresa Monteiro Fernandes, Pierre Schapira (2003)

Annales scientifiques de l'École Normale Supérieure

Tubenumgebungen Steinscher Räume.

Michael Schneider (1976)

Manuscripta mathematica

Tuboïdes dans $𝐂^{n}$ et généralisation d’un théorème de Cartan et Grauert

Jacques Bros, D. Iagolnitzer (1976)

Annales de l'institut Fourier

On introduit une classe de domaines dans $C_{(z)}^{n} = R_{(x)}^{n} \times R_{(y)}^{n}$ appelés tuboïdes. Un tuboïde $D = \cup_{x \in Ω} (x, D_{x})$ de profil $Λ = \cup_{x \in Ω} (x, Λ_{x})$ est un domaine de $C_{(z)}^{n}$ dont chaque fibre $D_{x}$ (dans $R_{(y)}^{n})$ admet $Λ_{x}$ comme cône tangent à l’origine.On montre dans la première partie que l’enveloppe d’holomorphie d’un tuboïde $\hat{D}$ de profil $\hat{Λ} = \cup_{x \in Ω} (x, {\hat{Λ}}_{x})$ où ${\hat{Λ}}_{x}$ est pour tout $x$ l’enveloppe convexe de $Λ_{x}$ . dans la deuxième partie, l’on montre alors que tout tuboïde $D$ dont le profil $Λ$ a toutes ses fibres $Λ_{x}$ convexes contient un tuboïde $D^{'}$ de même profil qui est de plus un domaine d’holomorphie....

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