Estimates for the Complex Monge-Ampère Equation on Hermitian and Balanced Manifolds
Tosatti, Valentino ; Weinkove, Ben
Asian J. Math., Tome 14 (2010) no. 1, p. 19-40 / Harvested from Project Euclid
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We generalize Yau’s estimates for the complex Monge-Ampère equation on compact manifolds in the case when the background metric is no longer Kähler. We prove $C^∞$ a priori estimates for a solution of the complex Monge-Ampère equation when the background metric is Hermitian (in complex dimension two) or balanced (in higher dimensions), giving an alternative proof of a theorem of Cherrier. We relate this to recent results of Guan-Li.
Publié le : 2010-03-15
Classification:  Complex Monge-Ampère equation,  Hermitian manifold,  balanced manifold,  32W20,  53C55,  32Q25 
@article{1286547517,
     author = {Tosatti, Valentino and Weinkove, Ben},
     title = {Estimates for the Complex Monge-Amp\`ere Equation on Hermitian and Balanced Manifolds},
     journal = {Asian J. Math.},
     volume = {14},
     number = {1},
     year = {2010},
     pages = { 19-40},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1286547517}
}

Tosatti, Valentino; Weinkove, Ben. Estimates for the Complex Monge-Ampère Equation on Hermitian and Balanced Manifolds. Asian J. Math., Tome 14 (2010) no. 1, pp.  19-40. http://gdmltest.u-ga.fr/item/1286547517/