We do have seen in an earlier lecture that $J$ equation's role in obtaining constant scalar curvature Kähler metric.
In this talk we study some special kind of test configuration, and we obtain the inequality
$$\Large\inf_{\omega\in c_1(L)}||\Lambda_\omega\alpha-c||_{L^2}\geq \sup_{\chi\text{ test-config}}-\frac{F_\alpha(\chi)}{||\chi||}.$$