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
View on Springer
projecteuclid.org
502 Citations
Highly Influential Citations
24
Background Citations
91
Methods Citations
41
Results Citations
11

502 Citations

On the singularities of the Bergman projections for lower energy forms on complex manifolds with boundary
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…
Bergman–Toeplitz operators on weakly pseudoconvex domains
We prove that for certain classes of pseudoconvex domains of finite type, the Bergman–Toeplitz operator $$T_{\psi }$$Tψ with symbol $$\psi =K^{-\alpha }$$ψ=K-α maps from $$L^{p}$$Lp to $$L^{q}$$Lq…
Condition R and proper holomorphic maps between equidimensional product domains
Special Toeplitz operators on strongly pseudoconvex domains
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…
On the Classification of Normal Stein Spaces and Finite Ball Quotients With Bergman–Einstein Metrics
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…
Bergman–Einstein metrics, a generalization of Kerner’s theorem and Stein spaces with spherical boundaries
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…
Boundary singularity of Poisson and harmonic Bergman kernels
Bergman Kernel and Kähler Tensor Calculus
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…
Infimum of the spectrum of Laplace–Beltrami operator on a bounded pseudoconvex domain with a Kähler metric of Bergman type
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…
Regularity and boundary behavior of solutions to complex Monge–Ampère equations
In the theory of holomorphic functions of one complex variable it is often useful to study subharmonic functions. The subharmonic can be described using the Laplace operator. When one studies…
...
...

References

SHOWING 1-10 OF 10 REFERENCES
Über die 1. und 2. Ableitungen der Bergmanschen Kernfunktion und ihr Randverhalten
The Bergman kernel function. Differentiability at the boundary
Topologische Fortsetzung biholomorpher Funktionen auf dem Rande bei beschränkten streng-pseudokonvexen Gebieten im ℂn mitC∞-Rand
L2 estimates and existence theorems for the $$\bar \partial $$ operator
Das Randverhalten der Bergmanschen Kernfunktion und Metrik in streng pseudo-konvexen Gebieten
The Neumann problem for the Cauchy-Riemann complex
Part explanation of important recent work, and part introduction to some of the techniques of modern partial differential equations, this monograph is a self-contained exposition of the Neumann…
Boundary Behavior of Holomorphic Functions of Several Complex Variables.
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
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…