Results 101 to 110 of about 3,934 (132)

Volume Approximations of Strongly Pseudoconvex Domains

The Journal of Geometric Analysis, 2016
In 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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Carleson Measures on Weakly Pseudoconvex Domains

The Journal of Geometric Analysis
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Oka's principle in pseudoconvex domains

Complex Variables, Theory and Application: An International Journal, 2001
Let x be a Banach space with a Schauder basis, for which the hypothesis (X) in the sense of Lempert is satisfied, and Ω be a pseudoconvex domain in x. Let L be an Abelian complex Lie group. A L or eL be, respectively, the sheaves over Ω of germs of holomorphic or continuous mappings into L and be the canonical inclusion. Then the mapping induced by the
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Pseudoconvex domains of semiregular type

1994
In this article we develop the geometric tools needed for obtaining more precise analytic information than known so-far on a relatively large class of bounded pseudoconvex domains Ω ⊂ ℂ n with C ∞-smooth boundary of finite type.
Klas Diederich, Gregor Herbort
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H p -Functions on Strictly Pseudoconvex Domains

American Journal of Mathematics, 1976
Introduction. In this paper we study some questions concerning HP-functions on strictly pseudoconvex domains in CN. For the most part, the results we obtain are analogues of well known theorems in one variable. The first section is devoted to a few preliminaries about the Hardy classes on domains in CN.
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Invariant metrics on pseudoconvex domains

1984
Let Ω be a bounded domain in ℂn. Each of the metrics of Bergman, Caratheodory, and Kobayashi assigns a positive number to a given non-zero tangent vector X above a point z in Ω. This assignment is invariant in the sense that if f is a biholomorphism of Ω onto another bounded domain Ω′, then the metric applied to X equals the value of the metric on Ω ...
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Pseudoconvex Domains and Oka’s Theorem

2016
In this chapter we deal with pseudoconvex domains. In Chap. 4 we saw that the Oka–Cartan Fundamental Theorem holds on holomorphically convex domains, and in Chap. 5 that a holomorphically convex domain is equivalent to a domain of holomorphy. These domains are shown to be pseudoconvex (Cartan–Thullen). The converse (Levi’s problem) was proved by K. Oka
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q-pseudoconvex and q-complete domains

1984
Main result: If D is a domain with \(C^ 2\) boundary in a Stein manifold M and D has q-pseudoconvex boundary, then D is q-complete. The proof uses a reduction (by embedding and tubular neighbourhood) to the case \(M={\mathbb{C}}^ N\).
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On pseudoconvexity of Reinhardt domains

1996
Für Reinhardt'sche Gebiete im \(\mathbb{C}^2\) wird der Zusammenhang zwischen Pseudokonvexität und logarithmischer Konvexität diskutiert.
M. Landucci, SPIRO, Andrea
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Domains of Holomorphy and Pseudoconvexity

1986
In 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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