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I need to show that the property of being a domain of holomorphy is the same as being a holomorphically convex domain (this result is known as Cartan-Thullen theorem). However, the proofs I found in textbooks (e.g. Shabat) look ugly and are hard to digest.

Is there a reference with a better proof? Can you share your intuition on looking at this result? Thanks in advance.

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    $\begingroup$ In my experience the proofs are hard to digest. I don't think there is any getting around it. Beauty is in the eye of the beholder of course. $\endgroup$
    – Steven Gubkin
    Commented Jan 27, 2021 at 23:06

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I can't really anticipate what you will find ugly and hard to digest, but at least I found the proof in Jiří Lebls book "Tasty Bits of Several Complex Variables", Theorem 2.6.3, to be nicely presented (but I don't think it is very different from what is found in many other sources).

In general, I think this book is a very friendly introduction to basic results in SCV like this, and it is freely available at https://www.jirka.org/scv/

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  • $\begingroup$ Thanks a lot! It’s indeed friendly. $\endgroup$
    – Nicholas S
    Commented Jan 28, 2021 at 16:03

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