Estimates for the complex Monge-Amp\`ere equation on Hermitian and balanced manifolds
Tosatti, Valentino ; Weinkove, Ben
arXiv, 0909.4496 / Harvested from arXiv
Text on arXiv
We generalize Yau's estimates for the complex Monge-Ampere equation on compact manifolds in the case when the background metric is no longer Kahler. We prove $C^{\infty}$ a priori estimates for a solution of the complex Monge-Ampere 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 : 2009-09-24
Classification:  Mathematics - Differential Geometry,  Mathematics - Complex Variables 
@article{0909.4496,
     author = {Tosatti, Valentino and Weinkove, Ben},
     title = {Estimates for the complex Monge-Amp\`ere equation on Hermitian and
  balanced manifolds},
     journal = {arXiv},
     volume = {2009},
     number = {0},
     year = {2009},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0909.4496}
}

Tosatti, Valentino; Weinkove, Ben. Estimates for the complex Monge-Amp\`ere equation on Hermitian and
  balanced manifolds. arXiv, Tome 2009 (2009) no. 0, . http://gdmltest.u-ga.fr/item/0909.4496/