# The Bergman kernel and biholomorphic mappings of pseudoconvex domains

@article{Fefferman1974TheBK,
title={The Bergman kernel and biholomorphic mappings of pseudoconvex domains},
author={Charles Fefferman},
journal={Inventiones mathematicae},
year={1974},
volume={26},
pages={1-65}
}
• C. Fefferman
• Published 1 March 1974
• Mathematics
• Inventiones mathematicae
502 Citations
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• Mathematics
• 2019
Let $M$ be a complex manifold of dimension $n$ with smooth boundary $X$. Given $q\in\{0,1,\ldots,n-1\}$, let $\Box^{(q)}$ be the $\ddbar$-Neumann Laplacian for $(0,q)$ forms. We show that the
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Mathematische Zeitschrift
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Toeplitz operators on strongly pseudoconvex domains in Cn, constructed from the Bergman projection and with symbol equal to a positive power of the distance to the boundary, are considered. The
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In this paper, we study the Bergman metric of a finite ball quotient $\mathbb{B}^n/\Gamma$, where $\Gamma \subseteq \mathrm{Aut}(\mathbb{B}^n)$ is a finite, fixed point free, abelian group. We prove
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Abstract We give an affirmative solution to a conjecture of Cheng proposed in 1979 which asserts that the Bergman metric of a smoothly bounded strongly pseudoconvex domain in ℂ n , n ≥ 2
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Fefferman [22] initiated a program of expressing the asymptotic expansion of the boundary singularity of the Bergman kernel for strictly pseudoconvex domains explicitly in terms of boundary
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• Mathematics
• 2010
The research in paper is a continuation of the work of Li and Wang [10–12] who studied upper estimates for λ1 = λ1(Δg), the bottom of the spectrum of Laplace–Beltrami operator on a complete
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This book has as its subject the boundary value theory of holomorphic functions in several complex variables, a topic that is just now coming to the forefront of mathematical analysis. For one
Boundary behavior of the Carathéodory and Kobayashi metrics on strongly pseudoconvex domains in C[n] with smooth boundary
The Carathe'odory and Kobayashi distance functions on a bounded domain G in Cn have related infinitesimal forms. These are the Caratheodory and Kobayashi metrics. They are denoted by F(z, t) Oength
Parametrices and estimates for the $\bar \partial _b$ complex on strongly pseudoconvex boundaries
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• 1974
0. Introduction. Here we briefly sketch the background of the problem to be considered, and refer to Folland-Kohn [4] for definitions and proofs. Let X be the boundary of a strongly pseudoconvex
BOUNDARY BEHAVIOR OF THE CARATHÉODORY, KOBAYASHI, AND BERGMAN METRICS ON STRONGLY PSEUDOCONVEX DOMAINS IN C" WITH SMOOTH BOUNDARY
FB{zA) = {ds\z^)f in the notation of [4]. We consider the boundary behavior of these metrics for fixed £. The notable features are (i) the different limiting behavior in tangential and normal