We are restricting to graded Lagrangians, so as above, discs $\Sigma$ of type (i) have constant area under the flow, and cannot cause singularities.

We could generalize the programme of §3.2 to oriented Lagrangians rather than graded Lagrangians, so that $HF^{*}\bigl((L,E,b),(L^{\prime},E^{\prime},b^{\prime})\bigr)$ is ${\mathbin{\mathbb{Z}}}_{2}$-graded rather than ${\mathbin{\mathbb{Z}}}$-graded. In this case, curves of type (i) can cause singularities. For non-graded $L$, the area of curves $\Sigma$ of type (i) change under Lagrangian MCF by

where $\mu_{L}\in H^{1}(L,{\mathbin{\mathbb{R}}})$ is the Maslov class from §2.1, and $[\partial\Sigma^{t}]\in H_{1}(L,{\mathbin{\mathbb{R}}})$. As the r.h.s. of (3.11) is independent of $t$, if $\mu_{L}\cdot[\partial\Sigma^{0}]>0$ then unless other singularities happen first, the area of $\Sigma^{t}$ shrinks to zero at time $T=\mathop{\rm area}(\Sigma^{0})/(\mu_{L}\cdot[\partial\Sigma^{0}])$. So in the non-graded analogue of Principle 3.29, we should also include shrinking of type (i) discs $\Sigma$. Groh, Schwarz, Smoczyk and Zehmisch [22] used this idea to study singularities of Lagrangian MCF for monotone Lagrangians in ${\mathbin{\mathbb{C}}}^{m}$.