502 Citations
On the singularities of the Bergman projections for lower energy forms on complex manifolds with boundary
- 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…
Bergman–Toeplitz operators on weakly pseudoconvex domains
- MathematicsMathematische Zeitschrift
- 2018
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…
Special Toeplitz operators on strongly pseudoconvex domains
- Mathematics
- 2006
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
- Mathematics
- 2020
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
- Mathematics
- 2020
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…
Bergman Kernel and Kähler Tensor Calculus
- Mathematics
- 2013
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
- 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…
Regularity and boundary behavior of solutions to complex Monge–Ampère equations
- Mathematics
- 2002
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
Topologische Fortsetzung biholomorpher Funktionen auf dem Rande bei beschränkten streng-pseudokonvexen Gebieten im ℂn mitC∞-Rand
- Mathematics
- 1973
Das Randverhalten der Bergmanschen Kernfunktion und Metrik in streng pseudo-konvexen Gebieten
- Mathematics
- 1970
The Neumann problem for the Cauchy-Riemann complex
- Mathematics
- 1972
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.
- Mathematics
- 1972
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
- Mathematics
- 1975
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
- Mathematics
- 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
- Mathematics
- 1973
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…