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I am a graduate student trying to understand complex Monge-Ampere equations(mostly on complex manifolds with or without boundary, but also in C^n), but I can't put my hand on any monograph/textbook discussing this problem thoroughly. Is there anything out there that could help me? If there isn't, can any of you folks tell me with what articles I should start my reading?

Any piece of information is appreciated.

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    $\begingroup$ I think you should start with Maciej Klimek's book "Pluripotential theory". Try it, and you'll tell me! $\endgroup$
    – diverietti
    Dec 16, 2011 at 6:57

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Kołodziej's and Klimek's books are very good, and Demailly's online book also has useful material. You can also try with Zbigniew Błocki's lecture notes

http://gamma.im.uj.edu.pl/~blocki/publ/ln/wykl.pdf

http://gamma.im.uj.edu.pl/~blocki/publ/ln/tln.pdf

This classical paper of Caffarelli-Kohn-Nirenberg-Spruck is also a must!

For the case of compact Kähler manifolds, apart from Błocki's notes above, I would also recommend Siu's book and this Asterisque book in French.

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  • $\begingroup$ Thanks a lot. Seems like I have a lot of reading to do this winter :) $\endgroup$
    – Hammerhead
    Dec 20, 2011 at 18:30
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Klimek's book is a good starting point for the theory in $\mathbb{C}^n$. For manifolds, go to:

Kołodziej, Sławomir The complex Monge-Ampère equation and pluripotential theory. Mem. Amer. Math. Soc. 178 (2005), no. 840, x+64 pp.

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Though it doesn't focus exclusively on complex Monge-Ampere equations, I learnt a lot from Gilbarg and Trudinger's book "Elliptic pdes of second order".

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It's rather too late. However, Vincent Guedj and Ahmed Zeriahi, Degenerate Complex Monge-Ampere Equations seems to be a very carefully written book.

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