MAXIMUM PRINCIPLE -- Part 1 -- Core Theorems of Complex Analysis

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Part 2: • The Schwarz Lemma -- C...
Part 3: • Liouville's theorem --...
In this video, we give a proof of the Maximum Principle, which is a monumental result in the subject of complex analysis. The maximum principle is also referred to as the maximum modulus principle, and states that the modulus of a holomorphic function cannot achieve an interior maximum. The proof we give here is elementary, albeit requiring the less-elementary open mapping theorem, and is due to the late Professor Alexander Isaev.
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These videos are separate from my research and teaching roles at the Australian National University, University of Sydney, and Beijing University.

[@KyleBroder]

👍 To support the channel, hit the like button and subscribe.

[@michelgeidorf3387]

keep the awesome uploads coming! :)

[@KyleBroder]

Will do! Thanks for the kind words 🙏

[@jamesking8043]

Video number 2! If only I watched the video on proof by contradiction.

[@bobnob4393]

As someone who's learning complex analysis I wish it was explained more in leymans terms, i feel like the graph was more useful in explaining this concept than all the jargon before it but i'm still pretty lost. I'm so grateful for you putting this content out there but i feel no better understanding from watching it

[@KyleBroder]

Complex analysis is not easy, you have to sit with ideas and struggle with them. That's where the learning happens.

[@thomasstriem2173]

brilliant! Just brilliant

[@KyleBroder]

🙏

[@jerrysinger2985]

Excellent!

[@KyleBroder]

Glad you liked it!

[@kammadyhr2943]

Thank you!

[@kaixianglai]

so clear！

[@changtillend5718]

Thank you ...

[@tretolien1195]

After seeing the proof of this theorem I am now very sad, like danm there exists no complex differentiable functions on any region omega where the maximum isen't trivially bound to the edge, that just trivializes the whole space of complex differentiable functions to the point of them being almost boring... Just sad :(

[@KyleBroder]

It just says they're more rigid.

[@depressedguy9467]

Following stien book