Complete domains with respect to the Carathéodory distance. II
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- by Dong S. Kim PDF
- Proc. Amer. Math. Soc. 53 (1975), 141-142 Request permission
Abstract:
In [1] we have obtained the following result: Let $D$ be a bounded domain in ${{\text {C}}^n}$. Suppose there is a compact subset $K$ of $D$ such that for every $x\epsilon D$ there is an analytic automorphism $f\epsilon \operatorname {Aut} (D)$ and a point $a\epsilon K$ such that $f(x) = a$. Then $D$ is a domain of bounded holomorphy, in the sense that $D$ is the maximal domain on which every bounded holomorphic function on $D$ can be continued holomorphically (cf. Narasimhan [2, Proposition 7, p. 127]). Here we shall give a stronger result: Under the same assumptions, $D$ is $c$-complete. We note that a $c$-complete domain is a domain of bounded holomorphy, in particular, a domain of holomorphy. A domain of bounded holomorphy, however, need not be $c$-complete.References
- Dong S. Kim, Complete domains with respect to the Carathéodory distance, Proc. Amer. Math. Soc. 49 (1975), 169–174. MR 367297, DOI 10.1090/S0002-9939-1975-0367297-3
- Raghavan Narasimhan, Several complex variables, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, Ill.-London, 1971. MR 0342725
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 53 (1975), 141-142
- MSC: Primary 32H15
- DOI: https://doi.org/10.1090/S0002-9939-1975-0382731-0
- MathSciNet review: 0382731