Invariant metrics and peak functions on pseudoconvex domains of homogeneous finite diagonal type

1992 ◽  
Vol 209 (1) ◽  
pp. 223-243 ◽  
Author(s):  
Gregor Herbort
Keyword(s):  
Pseudoconvex Domains ◽  
Invariant Metrics ◽  
Peak Functions

scholarly journals Comparison of invariant metrics and distances on strongly pseudoconvex domains and worm domains

2018 ◽  
Vol 292 (3-4) ◽  
pp. 879-893 ◽  
Author(s):  
Filippo Bracci ◽  
John Erik Fornæss ◽  
Erlend Fornæss Wold
Keyword(s):  
Pseudoconvex Domains ◽  
Invariant Metrics ◽  
Strongly Pseudoconvex Domains ◽  
Worm Domains

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

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