On compactness of Kähler metrics with bounded entropy and bounded $L^{2n+1}$ scalar curvature

Abstract

In their seminal work (\cite{CC}, \cite{CC2}), Chen and Cheng proved apriori estimates for the constant scalar curvature metrics on compact Kähler manifolds. They also proved $C^{3,\alpha }$ estimate for the potential of the \ka metrics under boundedness assumption on the scalar curvature and the entropy. The goal of this short note is to slightly relax the boundedness condition on the scalar curvature.

arXiv commentThe argument for higher order estimates is wrong