Displaying similar documents to “Bergman completeness of complete circular domains”

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.

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...

Bergman coordinates

Steven R. Bell (2006)

Studia Mathematica

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Various incarnations of Stefan Bergman's notion of representative coordinates will be given that are useful in a variety of contexts. Bergman wanted his coordinates to map to canonical regions, but they fail to do this for multiply connected regions. We show, however, that it is possible to define generalized Bergman coordinates that map multiply connected domains to quadrature domains which satisfy a long list of desirable properties, making them excellent candidates to be called Bergman...

Completeness of the Bergman metric on non-smooth pseudoconvex domains

Bo-Yong Chen (1999)

Annales Polonici Mathematici

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We prove that the Bergman metric on domains satisfying condition S is complete. This implies that any bounded pseudoconvex domain with Lipschitz boundary is complete with respect to the Bergman metric. We also show that bounded hyperconvex domains in the plane and convex domains in n are Bergman comlete.

Biholomorphic invariants related to the Bergman functions

Maciej Skwarczyński

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CONTENTSPRELIMINARY REMARKS........................................................................................ 5 Introduction..................................................................................................... 5 Basic definitions, examples and facts............................................................... 8I. LU QI-KENQ DOMAINS........................................................................................... 13 Some properties of Lu Qi-keng domains.....................................................

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 ) 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 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.