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One example of the boundary behaviour of biholomorphic transformations

Author: B. L. Fridman
Journal: Proc. Amer. Math. Soc. 89 (1983), 226-228
MSC: Primary 32H99; Secondary 32F15
MathSciNet review: 712627
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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.

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  • [1] S. Bell, Smooth bounded strictly and weakly pseudoconvex domains cannot be biholomorphic, Bull. Amer. Math. Soc. (N.S.) 4 (1981), 119-120. MR 590824 (82b:32039)
  • [2] S. Bell and D. Cathlin, Proper holomorphic mappings extend smoothly to the boundary, Bull. Amer. Math. Soc. (N.S.) 7 (1982), 269-272. MR 656209 (83d:32024)
  • [3] K. Diederich and J. E. Fornaess, Smooth extendability of proper holomorphic mappings, Bull. Amer. Math. Soc. (N.S.) 7 (1982), 264-268. MR 656208 (83f:32022)
  • [4] C. Fefferman, The Bergman kernel and biholomorphic mappings of pseudoconvex domains, Invent. Math. 26 (1974), 1-65. MR 0350069 (50:2562)
  • [5] B. L. Fridman, On a class of analytic polyhedra, Dokl. Akad. Nauk SSSR 242 (1978); English transl., Soviet Math. Dokl. 19 (1979), 1258-1261. MR 510253 (80b:32014)
  • [6] G. Henkin, An analytic polyhedron is not holomorphically equivalent to a strictly pseudoconvex domain, Soviet. Math. Dokl. 14 (1973), 858-862. MR 0328125 (48:6467)
  • [7] S. G. Krantz, Function theory of several complex variables, Wiley, New York, 1982. MR 635928 (84c:32001)

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