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Let and be strictly pseudoconvex domains in with real analytic boundaries and , and let be a neighborhood of the point with connected. Assume that the mapping is holomorphic in , in , and that . The author proves that can be holomorphically continued to . If the domain is a sphere and is simply connected, then extends to a biholomorphic mapping from onto .Bibliography: 12 titles.
S I Pinčuk (Wed,) studied this question.