In contrast to §3.2, Lagrangian MCF $\{L^{t}:t\in[0,T)\}$ of compact, immersed, graded Lagrangians $L$ or branes $(L,E)$ with $HF^{*}$ obstructed in a Calabi–Yau $m$-fold may develop finite time singularities at $t=T,$ such that one cannot continue the flow for $t>T$ in graded LMCF, even after a surgery.

A typical way in which this occurs is that for $t\in(T-\epsilon,T),$ there exists a ‘teardrop’ $J$-holomorphic curve $\Sigma^{t}$ with boundary in $L^{t}$ of the form shown in Figure 2.3, and $\mathop{\rm area}(\Sigma^{t})\rightarrow 0$ as $t\rightarrow T,$ where $\Sigma^{t}$ causes $L^{t}$ to have $HF^{*}$ obstructed if $\mathop{\rm area}(\Sigma^{t})$ is small enough.

In dimension $m\geqslant 2,$ this should be possible for $L^{0}$ with arbitrarily small phase variation.