Please use this identifier to cite or link to this item: https://ah.nccu.edu.tw/handle/140.119/120125

 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),77-82AMS MathSciNet:MR1007877 Data Type: article Appears in Collections: [應用數學系] 期刊論文

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