(Floer theoretic obstruction, multiple Lagrangian case) Assume the automatic transversality and the positivity condition hold for the bordism current $\mathcal{C}$. Assume the destabilizing condition

$$\hat{\theta}_{1}>\hat{\theta}_{2}>\ldots>\hat{\theta}_{N},\quad\hat{\theta}_{i}=\arg\int_{L_{i}}\Omega.$$

Then the Lagrangian phase angle of $L$ has a lower bound on its oscillation:

$$\sup_{L}\theta_{L}\geq\hat{\theta}_{1},\quad\inf_{L}\theta_{L}\leq\hat{\theta}_{N},$$

(35)

and morever the J-volume of $L$ has a nontrivial lower bound

$$\text{Vol}_{J}(L)=\int_{L}e^{-i\theta}\Omega\geq\sum_{1}^{N}|\int_{L_{i}}\Omega|.$$

(36)