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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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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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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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