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Title:	Some remarks on the indicatrix of invariant metric on convex domains
Authors:	陳天進 Chen, Ten Ging
Contributors:	應數系
Date:	1989-03
Issue Date:	2018-09-25 16:21:46 (UTC+8)
Abstract:	If $\\Omega$ is a domain in $\\bold C^n$ and if (for $p\\in\\Omega$, $X\\in \\bold C^n)$ $F_\\Omega(p;X)$ denotes the infinitesimal Kobayashi metric on $\\Omega$, then the indicatrix of $\\Omega$ at $p$ is the set $I_\\Omega(p)=\\{X\\in\\bold C^n\\: F_\\Omega(p;X)<1\\}$. In this paper the author answers one of the questions posed by S. Kobayashi [Bull. Amer. Math. Soc. 82 (1976), no. 3, 357–416; MR0414940]. Namely, he proves that if $\\Omega$ is a (bounded or unbounded) convex domain in $\\bold C^n$, then the indicatrix of $\\Omega$ is also a convex domain in $\\bold C^n$. As an application, the author also gives an elementary proof of the classical result due to Poincaré concerning the nonequivalence of the unit ball and the polydisc in $\\bold C^n$.
Relation:	Chinese Journal of Mathematics,17(1),77-82 AMS MathSciNet:MR1007877
Data Type:	article
Appears in Collections:	[應用數學系] 期刊論文

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