Remarks on a result of Chen-Cheng

Abstract

In their seminal work, Chen and Cheng proved a priori estimates for the constant scalar curvature metrics on compact Kähler manifolds. They also prove C3,α{C}^{3,\alpha }-estimate for the potential of the Kähler metrics under boundedness assumption on the scalar curvature and the entropy. The goal of this article is to replace the uniform boundedness of the scalar curvature to the Lp{L}^{p}-boundedness of the scalar curvature.

Keywords

• calabi flow
• chen-cheng estimate
• scalar curvature
• 53b35