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On hyperbolicity of pseudoconvex Reinhardt domains
Archiv Der Mathematik, 1999A Reinhardt domain is a subset \(D\) of \(n-\)dimensional complex space \(C^n\) such that for all \(z=(z_1,\dots,z_n)\in D\) and \(|\lambda_1|=\dots=|\lambda_n|=1\), we have \((|\lambda_1|z_1, \dots,|\lambda_n|z_n)\in D\). The author gives a characterization of Kobayashi hyperbolicity for pseudo-convex Reinhardt domains. He proves that such a domain is
Włodzimierz Zwonek
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Skew Carleson Measures in Strongly Pseudoconvex Domains [PDF]
Complex Analysis and Operator Theory, 2018 International audienceGiven a bounded strongly pseudoconvex domain D in C n with smooth boundary, we give a characterization through products of functions in weighted Bergman spaces of (λ, γ)-skew Carleson measures on D, with λ > 0 and γ > 1 − 1 n+1
Marco Abate +2 more
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Boundary Invariants of Pseudoconvex Domains
The Annals of Mathematics, 1984Let \(\Omega \subseteq {\mathbb{C}}^ n\) be a smoothly bounded pseudoconvex domain. A notion of multitype of a point \(P\in \partial \Omega\) is introduced. This term is defined in terms of directional derivatives of a defining function for \(\partial \Omega\).
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An Estimate for the Bergman Distance on Pseudoconvex Domains
The Annals of Mathematics, 1995Let \(D\) be a bounded pseudoconvex domain in \(\mathbb{C}^n\). Let \(\delta_D (z)\) denote the euclidean distance from \(z\) to the boundary of \(D\), and let \(\text{dist}_D (z,w)\) denote the Bergman distance between \(z\) and \(w\) with respect to \(D\).
Diederich, Klas, Ohsawa, Takeo
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Approximation on Pseudoconvex Domains
1980Here we discuss some problems in approximation which are related to the problem of finding pseudoconvex neighborhoods. Since we omit various topics, we refer the reader to the articles of Birtel [4], Henkin and Chirka [16], and Wells [28].
Eric Bedford, John Erik Fornaess
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On the projection of pseudoconvex domains
Mathematische Zeitschrift, 2000zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Volume Approximations of Strongly Pseudoconvex Domains
The Journal of Geometric Analysis, 2016In affine convex geometry, the volume approximation of a \(C^2\)-smooth convex body by polyhedra with at most \(n\) facets can be asymptotically estimated by \(n^{-2/(d-1)}\) times \((d+1)/(d-1)\)-th power of the integral of the Blaschke surface area measure on the boundary of the convex body. In this article, the author studies the complex analogue of
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Domains of Holomorphy and Pseudoconvexity
1986In 1906 F. Hartogs discovered the first example exhibiting the remarkable extension properties of holomorphic functions in more than one variable. It is this phenomenon, more than anything else, which distinguishes function theory in several variables from the classical one-variable theory.
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