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Biholomorphic maps determined on the boundary

Nozomu Mochizuki — 1977

Annales de l'institut Fourier

Let D be a bounded domain in C n such that the boundary b D is topologically S 2 n - 1 in R 2 n with a regular point; let f : D ˜ C n be a holomorphic map where D ˜ is a neighborhood of D . If f is one-to-one when restricted to b D , then f : D f ( D ) is biholomorphic.

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