Completeness of the Bergman metric on non-smooth pseudoconvex domains

Bo-Yong Chen

Displaying similar documents to “Completeness of the Bergman metric on non-smooth pseudoconvex domains”

On Bergman completeness of pseudoconvex Reinhardt domains

Włodzimierz Zwonek (1999)

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David W. Catlin (1988/89)

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Comparison of the Bergman and the Kobayashi Metric.

Klas Diederich, John Eric Fornaess (1980)

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The Hölder continuity of the Bergman projection and proper holomorphic mappings

Ewa Ligocka (1984)

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Some applications of the Bergman kernel to geometrical theory of functions

I. Ramadanov (1983)

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The Bergman kernel functions of certain unbounded domains

Friedrich Haslinger (1998)

Annales Polonici Mathematici

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We compute the Bergman kernel functions of the unbounded domains $Ω_{p} = (z^{'}, z) \in ℂ ² : z > p (z^{'})$ , where $p (z^{'}) = {| z^{'} |}^{α} / α$ . It is also shown that these kernel functions have no zeros in $Ω_{p}$ . We use a method from harmonic analysis to reduce the computation of the 2-dimensional case to the problem of finding the kernel function of a weighted space of entire functions in one complex variable.

Estimates of the Bergman kernel function on certain pseudoconvex domains in Cn.

Sanghyun Cho (1996)

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Estimates for the Bergman kernel and metric of convex domains in ℂⁿ

Nikolai Nikolov, Peter Pflug (2003)

Annales Polonici Mathematici

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Sharp geometrical lower and upper estimates are obtained for the Bergman kernel on the diagonal of a convex domain D ⊂ ℂⁿ which does not contain complex lines. It is also proved that the ratio of the Bergman and Carathéodory metrics of D does not exceed a constant depending only on n.

Bergman completeness of Zalcman type domains

Piotr Jucha (2004)

Studia Mathematica

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We give an equivalent condition for Bergman completeness of Zalcman type domains. This also solves a problem stated by Pflug.

The Bergman Kernel on Uniformly Extendable Pseudoconvex Domains.

Takeo Ohsawa, Klaus Diederich, Gregor Herbort (1985/86)

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Remarks on the Bergman kernel function of a worm domain

Ewa Ligocka (1998)

Studia Mathematica

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We use a recent result of M. Christ to show that the Bergman kernel function of a worm domain cannot be $C^{\infty}$ -smoothly extended to the boundary.

Completeness, Reinhardt domains and the method of complex geodesics in the theory of invariant functions

Włodzimierz Zwonek

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Our work is divided into five chapters. In Chapter I we introduce necessary notions and we present the most important facts that we shall use. We also present our main results. Chapter I covers the following topics: • holomorphically contractible families of functions and pseudometrics, their basic properties, product property, Lempert Theorem, notion of geodesic, problem of finding effective formulas for invariant functions and pseudometrics and geodesics, completeness...

On isometries of the Kobayashi and Carathéodory metrics

Prachi Mahajan (2012)

Annales Polonici Mathematici

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This article considers C¹-smooth isometries of the Kobayashi and Carathéodory metrics on domains in ℂⁿ and the extent to which they behave like holomorphic mappings. First we provide an example which suggests that 𝔹ⁿ cannot be mapped isometrically onto a product domain. In addition, we prove several results on continuous extension of C⁰-isometries f : D₁ → D₂ to the closures under purely local assumptions on the boundaries. As an application, we show that there is no C⁰-isometry between...