Carathéodory distance and convexity with respect to bounded holomorphic functions
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- by Su Shing Chen PDF
- Proc. Amer. Math. Soc. 39 (1973), 305-307 Request permission
Erratum: Proc. Amer. Math. Soc. 45 (1974), 468.
Abstract:
A characterization of connected complex manifolds with complete Carathéodory distances is obtained. Some basic facts concerning convexity of complex manifolds with respect to their algebras of bounded holomorphic functions are also given.References
- Su Shing Chen, Bounded holomorphic functions in Siegel domains, Proc. Amer. Math. Soc. 40 (1973), 539–542. MR 322211, DOI 10.1090/S0002-9939-1973-0322211-X
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- Helmut Horstmann, Zur Theorie der Funktionen mehrerer komplexen Veränderlichen: Carathéodorysche Metrik und Regularitätshüllen, Math. Ann. 108 (1933), no. 1, 208–217 (German). MR 1512845, DOI 10.1007/BF01452833
- Shoshichi Kobayashi, Hyperbolic manifolds and holomorphic mappings, Pure and Applied Mathematics, vol. 2, Marcel Dekker, Inc., New York, 1970. MR 0277770
- Karl Stein, Überlagerungen holomorph-vollständiger komplexer Räume, Arch. Math. (Basel) 7 (1956), 354–361 (German). MR 84836, DOI 10.1007/BF01900686
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 39 (1973), 305-307
- MSC: Primary 32E05; Secondary 32H15, 53C55
- DOI: https://doi.org/10.1090/S0002-9939-1973-0316750-5
- MathSciNet review: 0316750