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How can we define a smooth domain in $\mathbb{C}^2$ and a smooth boundary of bounded domain in $\mathbb{C}^2$?

{where $\mathbb{C}^2$ := Cartesian product of complex plane }

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    The same as you define any other smooth manifolds, I'd say. In particular, it depends on whether you want them to be complex-smooth or real-smooth.2012-12-26
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    Well, to expand a little, a domain is usually understood in analysis to be open and connected, so the adjective "smooth" seems rather superfluous in this case, unless you meant just a smooth manifold.2012-12-26

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