In section 5.3 we discussed that the Solomon functional should be non-increasing under Joyce’s LMCF. Suppose the flow extends weakly to Lagrangians in $\mathcal{L}$. The flow starting from a minimizer $L$ must have constant $\mathcal{S}(L_{t})$, but the evolution (57) would then force $\theta=\hat{\theta}$, namely $L$ is a special Lagrangian, and the flow is in fact constant.