Complete domains with respect to the Carathéodory distance. II

Author:
Dong S. Kim

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

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Abstract: In [1] we have obtained the following result: Let be a bounded domain in . Suppose there is a compact subset of such that for every there is an analytic automorphism and a point such that . Then is a domain of bounded holomorphy, in the sense that is the maximal domain on which every bounded holomorphic function on can be continued holomorphically (cf. Narasimhan [2, Proposition 7, p. 127]). Here we shall give a stronger result: Under the same assumptions, is -complete. We note that a -complete domain is a domain of bounded holomorphy, in particular, a domain of holomorphy. A domain of bounded holomorphy, however, need not be -complete.

**[1]**Dong S. Kim,*Complete domains with respect to the Carathéodory distance*, Proc. Amer. Math. Soc.**49**(1975), 169–174. MR**0367297**, https://doi.org/10.1090/S0002-9939-1975-0367297-3**[2]**Raghavan Narasimhan,*Several complex variables*, The University of Chicago Press, Chicago, Ill.-London, 1971. Chicago Lectures in Mathematics. MR**0342725**

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DOI:
https://doi.org/10.1090/S0002-9939-1975-0382731-0

Keywords:
-complete,
analytic automorphism,
bounded homogeneous domain

Article copyright:
© Copyright 1975
American Mathematical Society