Title: Reflection Principle in Higher Dimensions

The article discusses the use of the reflection principle in studying the following conjecture: Let $ D,D'\subset \CC ^{n}$ be domains with smooth real-analytic boundaries and $ f:D\rightarrow D' $ a proper holomorphic map. Then $ f$ extends holomorphically to a neighborhood of the closure of $ D$.

1991 Mathematics Subject Classification: 32H40, 32H99, 32D15

Keywords and Phrases: Proper holomorphic maps, reflection principle, Segre variety, holomorphic correspondences

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