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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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I think you should start with Maciej Klimek's book "Pluripotential theory". Try it, and you'll tell me! – diverietti Dec 16 '11 at 6:57
up vote 2 down vote accepted

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

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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Thanks a lot. Seems like I have a lot of reading to do this winter :) – The Common Crane Dec 20 '11 at 18:30

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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