A Remark On C^{2,α}-Regularity of the Complex Monge-Ampère Equation

Abstract

We prove the $C^{2,\alpha }$-regularity of the solution $u$ of the equation [\det(u_{\bar{k} j}) = f, \quad f^{1/n} \in C^α, \quad f \geq λ] under the assumption in upper bound of $\Delta u$. Our result settles down the regularity problem related to the paper \cite{Tian} (also see \cite{Zhang}).

References in corpus (1)

• The ${\mathcal{C}}^{2,\alpha }$ estimate of complex Monge-Ampere equation

Cited by in corpus (3)

• On the long time behaviour of the Conical Kähler- Ricci flows
• $C^{2,\alpha }$-estimate for Monge-Ampere equations with Hölder-continuous right hand side
• Removable singularities of the CscK metric