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Asymptotic Expansions of Invariant Metrics of Strictly Pseudoconvex Domains

Published online by Cambridge University Press:  20 November 2018

Siqi Fu
Siqi Fu*
Affiliation:
Department of Mathematics, Washington University, St. Louis, Missouri 63130, U.S.A. e-mail:sfu@pear.wustl.edu
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Abstract

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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

Keywords

32H1532E3032F15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 38 , Issue 2 , 01 June 1995 , pp. 196 - 206
Copyright
Copyright © Canadian Mathematical Society 1995

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