k-dimensional polydisk

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Complex manifold — In differential geometry, a complex manifold is a manifold with an atlas of charts to the open unit disk[1] in Cn, such that the transition maps are holomorphic. The term complex manifold is variously used to mean a complex manifold in the sense… … Wikipedia
Holomorphic function — A rectangular grid (top) and its image under a holomorphic function f (bottom). In mathematics, holomorphic functions are the central objects of study in complex analysis. A holomorphic function is a complex valued function of one or more complex … Wikipedia

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