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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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