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We study the classification of holomorphic isometric embeddings of the unit disk into polydisks. As a corollary of our results, we can give a complete classification when the target is the 2-disk and the 3-disk. We also prove that the holomorphic isometric embeddings between polydisks are induced by those of the unit disk into polydisks. © 2010 American Mathematical Society.published_or_final_versio

On holomorphic isometric embeddings of the unit disk into polydisks