Let $(\varphi,F)$ be a smooth solution to cscK, then there exists $p_{n}>0$, depending only on $n$, such that

(4.2)

$$\max_{M}|\nabla_{\varphi}F|_{\varphi}+\max_{M}(n+\Delta\varphi)\leq C_{4.2}.$$

Here $C_{4}$ depends only on $||F||_{0}$, $||n+\Delta\varphi||_{L^{p_{n}}(M)}$, and metric $g$(in the way described in Theorem 4.1).