A priori estimates for Donaldson's equation over compact Hermitian manifolds
arXiv:1210.0254 · doi:10.1007/s00526-013-0659-8
Abstract
In this paper we prove a priori estimates for Donaldson's equation $Ï\wedge(Ï+\sqrt{-1}\partial\bar{\partial}Ï)^{n-1}=e^{F}(Ï+\sqrt{-1}\partial\bar{\partial}Ï)^{n}$ over a compact Hermitian manifold X of complex dimension n, where $Ï$ and $Ï$ are arbitrary Hermitian metrics. Our estimates answer a question of Tosatti-Weinkove.
16 pages. Calculus of Variations and Partial Differential Equations, 2013