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

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DOI

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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     title = {Asymptotic {Expansions} of {Invariant} {Metrics} of {Strictly} {Pseudoconvex} {Domains}},
     journal = {Canadian mathematical bulletin},
     pages = {196--206},
     year = {1995},
     volume = {38},
     number = {2},
     doi = {10.4153/CMB-1995-028-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1995-028-9/}
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