scholarly journals Estimates of Invariant Metrics on Pseudoconvex Domains of Finite Type inC3

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Sanghyun Cho ◽  
Young Hwan You
Keyword(s):  
Finite Type ◽  
Pseudoconvex Domain ◽  
Pseudoconvex Domains ◽  
Invariant Metrics ◽  
Small Constant ◽  
Kobayashi Metrics

LetΩbe a smoothly bounded pseudoconvex domain inC3and assume thatz0∈bΩis a point of finite 1-type in the sense of D’Angelo. Then, there are an admissible curveΓ⊂Ω∪{z0}, connecting points  q0∈Ωandz0∈bΩ, and a quantityM(z,X), alongz∈Γ, which bounds from above and below the Bergman, Caratheodory, and Kobayashi metrics in a small constant and large constant sense.

Asymptotic Expansions of Invariant Metrics of Strictly Pseudoconvex Domains

1995 ◽  
Vol 38 (2) ◽  
pp. 196-206 ◽  
Author(s):  
Siqi Fu
Keyword(s):  
Continuous Function ◽  
Asymptotic Expansions ◽  
Pseudoconvex Domain ◽  
Smooth Boundary ◽  
Pseudoconvex Domains ◽  
Invariant Metrics ◽  
Kobayashi Metric ◽  
Signed Distance ◽  
Strictly Pseudoconvex Domain ◽  
Kobayashi Metrics

AbstractIn this paper we obtain the asymptotic expansions of the Carathéodory and Kobayashi metrics of strictly pseudoconvex domains with C∞ smooth boundaries in ℂn. The main result of this paper can be stated as following:Main Theorem. Let Ω be a strictly pseudoconvex domain with C∞ smooth boundary. Let FΩ(z,X) be either the Carathéodory or the Kobayashi metric of Ω. Let δ(z) be the signed distance from z to ∂Ω with δ(z) < 0 for z ∊ Ω and δ(z) ≥ 0 for z ∉ Ω. Then there exist a neighborhood U of ∂Ω, a constant C > 0, and a continuous function C(z,X):(U ∩ Ω) × ℂn -> ℝ such that and|C(z,X)| ≤ C|X| for z ∊ U ∩ Ω and X ∊ ℂn

Hankel Operators on Pseudoconvex Domains of Finite Type in ℂ2

1998 ◽  
Vol 50 (3) ◽  
pp. 658-672 ◽  
Author(s):  
Frédéric Symesak
Keyword(s):  
Hardy Space ◽  
Finite Type ◽  
Pseudoconvex Domain ◽  
Bergman Spaces ◽  
Hankel Operators ◽  
Weighted Bergman Spaces ◽  
Pseudoconvex Domains ◽  
Sufficient Condition ◽  
Schatten Class ◽  
Strictly Pseudoconvex Domain

AbstractThe aimof this paper is to study small Hankel operators h on the Hardy space or on weighted Bergman spaces,where Ω is a finite type domain in ℂ2 or a strictly pseudoconvex domain in ℂn. We give a sufficient condition on the symbol ƒ so that h belongs to the Schatten class Sp, 1 ≤ p < +∞.

scholarly journals Stability of Hölder estimates for on pseudoconvex domains of finite type in ℂ2

1997 ◽  
Vol 148 ◽  
pp. 23-37
Author(s):  
S. Cho ◽  
H. Ahn ◽  
S. Kim
Keyword(s):  
Finite Type ◽  
Pseudoconvex Domain ◽  
Pseudoconvex Domains ◽  
The Stability ◽  
Hölder Estimates

AbstractLet Ω be a smoothly bounded pseudoconvex domain in ℂ2 and let bΩ be of finite type m. Then we prove the stability of Hölder estimates for under some perturbations of bΩ. As an application, we prove the Mergelyan property with respect to () norms for 0 ≤ α < 1/m.

scholarly journals On proper holomorphic mappings from domains with T-action

1999 ◽  
Vol 154 ◽  
pp. 57-72 ◽  
Author(s):  
Bernard Coupet ◽  
Yifei Pan ◽  
Alexandre Sukhov
Keyword(s):  
Unit Circle ◽  
Finite Type ◽  
Holomorphic Mapping ◽  
Circular Domain ◽  
Holomorphic Mappings ◽  
Pseudoconvex Domains ◽  
Branch Locus ◽  
Proper Holomorphic Mapping ◽  
Proper Holomorphic Mappings

AbstractWe describe the branch locus of a proper holomorphic mapping between two smoothly bounded pseudoconvex domains of finite type in under the assumption that the first domain admits a transversal holomorphic action of the unit circle. As an application we show that any proper holomorphic self-mapping of a smoothly bounded pseudoconvex complete circular domain of finite type in is biholomorphic.

On the Bergman metric on bounded pseudoconvex domains an approach without the Neumann operator

2014 ◽  
Vol 25 (03) ◽  
pp. 1450025 ◽  
Author(s):  
Gregor Herbort
Keyword(s):  
Distance Function ◽  
Pseudoconvex Domain ◽  
Levi Form ◽  
Pseudoconvex Domains ◽  
Bergman Metric ◽  
Plurisubharmonic Functions ◽  
Euclidean Metric ◽  
Bounded Complex ◽  
Boundary Distance ◽  
Complex Gradient

Let 0 < ε ≤ ½ be fixed. We prove that on a bounded pseudoconvex domain D ⋐ ℂn the Bergman metric grows at least like [Formula: see text] times the euclidean metric, provided that on D there exists a family (φδ)δ of smooth plurisubharmonic functions with a self-bounded complex gradient (uniformly in δ), such that for any δ the Levi form of φδ has eigenvalues ≥ δ-2ε on the set {z ∈ D | δD(z) < δ}. Here, δD denotes the boundary-distance function on D.

scholarly journals Admissible limits of bloch functions on bounded strongly pseudoconvex domains

1996 ◽  
Vol 54 (1) ◽  
pp. 1-3
Author(s):  
Hu Zhangjian
Keyword(s):  
Pseudoconvex Domain ◽  
Bloch Function ◽  
Pseudoconvex Domains ◽  
Bloch Functions ◽  
Radial Limits ◽  
Strongly Pseudoconvex Domains ◽  
Almost Everywhere ◽  
Strongly Pseudoconvex Domain ◽  
Almost All

Let be a bounded strongly pseudoconvex domain with C2 boundary . In this paper we prove that for a Bloch function in the existance of radial limits at almost all implies the existence of admissible limits almost everywhere on .

Sign in / Sign up

Export Citation Format

Share Document