A priori estimates for Donaldson's equation over compact Hermitian manifolds

Abstract

In this paper we prove a priori estimates for Donaldson's equation $\omega \wedge (\chi +\sqrt{-1}\partial \bar{\partial }\phi {)}^{n-1}=e^F(\chi +\sqrt{-1}\partial \bar{\partial }\phi {)}^n$ over a compact Hermitian manifold X of complex dimension n, where $\omega$ and $\chi$ are arbitrary Hermitian metrics. Our estimates answer a question of Tosatti-Weinkove.

16 pages. Calculus of Variations and Partial Differential Equations, 2013

References in corpus (1)

• The Chern-Ricci flow on complex surfaces

Cited by in corpus (2)

• $C^{2,\alpha }$ estimates for nonlinear elliptic equations in complex and almost complex geometry
• $C^{2,\alpha }$ regularities and estimates for nonlinear elliptic and parabolic equations in geometry