One example of the boundary behaviour of biholomorphic transformations
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- by B. L. Fridman PDF
- Proc. Amer. Math. Soc. 89 (1983), 226-228 Request permission
Abstract:
Two biholomorphically equivalent domains ${\Omega _1}$, ${\Omega _2} \subset {{\mathbf {C}}^2}$ with piecewise smooth boundaries and with the following property are constructed. If $F:{\Omega _1} \to {\Omega _2}$ is any biholomorphic transformation then neither $F$ nor ${F^{ - 1}}$ can be extended continuously to the boundary.References
- Steven Bell, Smooth bounded strictly and weakly pseudoconvex domains cannot be biholomorphic, Bull. Amer. Math. Soc. (N.S.) 4 (1981), no. 1, 119–120. MR 590824, DOI 10.1090/S0273-0979-1981-14878-3
- Steven Bell and David Catlin, Proper holomorphic mappings extend smoothly to the boundary, Bull. Amer. Math. Soc. (N.S.) 7 (1982), no. 1, 269–272. MR 656209, DOI 10.1090/S0273-0979-1982-15031-5
- Klas Diederich and John Erik Fornæss, Smooth extendability of proper holomorphic mappings, Bull. Amer. Math. Soc. (N.S.) 7 (1982), no. 1, 264–268. MR 656208, DOI 10.1090/S0273-0979-1982-15029-7
- Charles Fefferman, The Bergman kernel and biholomorphic mappings of pseudoconvex domains, Invent. Math. 26 (1974), 1–65. MR 350069, DOI 10.1007/BF01406845
- B. L. Fridman, A class of analytic polyhedra, Dokl. Akad. Nauk SSSR 242 (1978), no. 5, 1020–1022 (Russian). MR 510253
- G. M. Henkin, An analytic polyhedron is not holomorphically equivalent to a strictly pseudoconvex domain, Dokl. Akad. Nauk SSSR 210 (1973), 1026–1029 (Russian). MR 0328125
- Steven G. Krantz, Function theory of several complex variables, Pure and Applied Mathematics, John Wiley & Sons, Inc., New York, 1982. MR 635928
Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 89 (1983), 226-228
- MSC: Primary 32H99; Secondary 32F15
- DOI: https://doi.org/10.1090/S0002-9939-1983-0712627-8
- MathSciNet review: 712627