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:I don't think it is standard anywhere to refer to the theory of complex functions of several variables as "domains of holomorphy theory" so Wikipedia should definitely avoid presenting that as the main name of the subject. As you point out however, people do refer to "several complex variables" and that is the title of the main book on the subject, so that is surely the better name for the article. I think we probably agree that the area is different enough in flavour to complex analysis of a single variable that it deserves its own article. I wouldn't be opposed to merging with [[complex analysis]], which is quite a thin article, but I don't think there is any particular need to. In particular I think complex analysis of a single variable gets a very different (and much broader) treatment pedagogically, and that is an article looked at frequently by people who are not pure mathematicians interested in several complex variables (engineers, physicists) and presenting all the definitions on that page in their largest generality would serve more to obfuscate the point rather than elucidate it for most visitors. Just my two cents. Thank you for improving the articles in complex analysis! [[User:Tazerenix|Tazerenix]] ([[User talk:Tazerenix|talk]]) 05:53, 23 December 2020 (UTC)
::Thank you very much for teaching me. Thanks for giving me many interesting examples of other manifolds. Sure, it seems too narrow, so I turn the suggestion into a section redirect to the ___domain of holomorphism. Then, I will modify the lead sentence and correct it to say, "One of the reasons why this field has come to be studied is that the boundary does not become a natural boundary." thanks!--[[User:SilverMatsu|SilverMatsu]] ([[User talk:SilverMatsu|talk]]) 08:01, 23 December 2020 (UTC)
It may be better to say that this page is a theory of Several complex variables function rather than a function theory of Several complex variables. If the analysis part of this page gets too big, it seems that it can be divided into function theory of Several complex variables. I'll look at the redirects on this page. thanks!--[[User:SilverMatsu|SilverMatsu]] ([[User talk:SilverMatsu|talk]]) 06:20, 24 December 2020 (UTC)
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