For any $p>0$, there exist constants $\alpha(p)>0$, $C(p)>0$, so that

(3.1)

$$\int_{M}e^{-\alpha(p)F}(n+\Delta\varphi)^{p}dvol_{g}\leq C(p).$$

Here $\alpha(p)$ depends only on $p$(can be explicitly calculated). The constant $C_{p}$ depends only on $p$, $||\varphi||_{0}$, the upper bound of Ricci form, lower bound of the bisectional curvature, and volume of $g$.