Geodesic
Asymptotic Expansions of Invariant Metrics of Strictly Pseudoconvex Domains
Canadian mathematical bulletin, Tome 38 (1995) no. 2, pp. 196-206

Voir la notice de l'article provenant de la source Cambridge University Press

In 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
DOI : 10.4153/CMB-1995-028-9
Mots-clés : 32H15, 32E30, 32F15 
Fu, Siqi. Asymptotic Expansions of Invariant Metrics of Strictly Pseudoconvex Domains. Canadian mathematical bulletin, Tome 38 (1995) no. 2, pp. 196-206. doi: 10.4153/CMB-1995-028-9
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