Results 51 to 60 of about 3,739 (136)

Compactness of the Complex Green Operator on C¹ Pseudoconvex Boundaries in Stein Manifolds

Mathematics
We study compactness for the complex Green operator Gq associated with the Kohn Laplacian □b on boundaries of pseudoconvex domains in Stein manifolds. Let Ω⋐X be a bounded pseudoconvex domain in a Stein manifold X of complex dimension n with C1 boundary.
Abdullah Alahmari, Emad Solouma, Marin Marin, A. F. Aljohani, Sayed Saber   +4 more
doaj   +1 more source

Peak Points for Pseudoconvex Domains: A Survey [PDF]

Journal of Geometric Analysis, 2008
This paper surveys results concerning peak points for pseudoconvex domains. It includes results of Laszlo that have not been published elsewhere.
openaire   +2 more sources

Compactness of commutators of Toeplitz operators on q-pseudoconvex domains

Electronic Journal of Differential Equations, 2018
Let $\Omega$ be a bounded q-pseudoconvex domain in $\mathbb{C}^n$, $n \geq 2$ and let $1 \leq q \leq n-1$. If $\Omega$ is smooth, we find sufficient conditions for the $\overline\partial$-Neumann operator to be compact.
Sayed Saber
doaj  

Geometry of analytic continuation on complex manifolds – history, survey, and report

Complex Manifolds
Beginning with the state of art around 1953, solutions of the Levi problem on complex manifolds will be recalled at first up to Takayama’s result in 1998.
Ohsawa Takeo
doaj   +1 more source

On the boundary behavior of the holomorphic sectional curvature of the Bergman metric

Le Matematiche, 2006
We obtain a conceptually new differential geometric proof of P. F. Klembeck’s result (cf. [9]) that the holomorphic sectional curvature k g (z ) of the Bergman metric of a strictly pseudoconvex domain Ω ⊂ ℂ n approaches −4/(n + 1 ...
Elisabetta Barletta
doaj  

Variations of pseudoconvex domains

Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1983
A connected Hausdorff space E together with a locally homeomorphic map \(\pi\) of E to \({\mathbb{R}}^ m\) is called an unramified covering domain over the space \({\mathbb{R}}^ m\). Suppose D is such a domain and \(D_ p\) is a sequence of relatively compact subdomains of D such that \(x^ 0\in D_ 1\), \(D_ p\subset D_{p+1}\), \(\cup^{\infty}_{p=1}D_ p ...
openaire   +3 more sources

Smoothness to the boundary of biholomorphic mappings

, 2014
Under a plausible geometric hypothesis, we show that a biholomorphic mapping of smoothly bounded, pseudoconvex domains extends to a diffeomorphism of the ...
Krantz, Steven G.
core   +1 more source

Kähler–Einstein metrics on strictly pseudoconvex domains [PDF]

Annals of Global Analysis and Geometry, 2012
The metrics of S. Y. Cheng and S.-T. Yau are considered on a strictly pseudoconvex domains in a complex manifold. Such a manifold carries a complete K hler-Einstein metric if and only if its canonical bundle is positive. We consider the restricted case in which the CR structure on $\partial M$ is normal. In this case M must be a domain in a resolution
openaire   +3 more sources

Worm Domains are not Gromov Hyperbolic. [PDF]

J Geom Anal, 2023
Arosio L, Dall'Ara GM, Fiacchi M.
europepmc   +1 more source

Szegő Kernel Asymptotics on Complete Strictly Pseudoconvex CR Manifolds. [PDF]

J Geom Anal, 2022
Hsiao CY, Marinescu G, Wang H.
europepmc   +1 more source