Example 2.16 described a family of Lagrangian MCF translators $L$ in ${\mathbin{\mathbb{C}}}^{m}$ given in equation (2.10), asymptotic to the union of two Lagrangian planes $\Pi_{0},\Pi_{\boldsymbol{\phi}}\cong{\mathbin{\mathbb{R}}}^{m}$ intersecting in ${\mathbin{\mathbb{R}}}$. We have sketched $L$ in Figure 3.9 (not easy to draw in only two dimensions).

We indicate the intersection of $L$ with the $z_{m}$-axis, the curve

which bounds a noncompact $J$-holomorphic curve $\Sigma$ in the $z_{m}$-axis as shown.

We will try and describe a type II singularity of Lagrangian MCF $\{L^{t}:t\in[0,T)\}$ with a singularity at $x\in M$ modelled on these LMCF translators $L$, using Principle 3.9(b). Identifying $M$ with $T_{x}M\cong{\mathbin{\mathbb{C}}}^{m}$ near $x\in M$, each $L^{t}$ should to ‘first order’ approximate an LMCF translator $L$ from Example 2.16, and as $t\rightarrow T$ these LMCF translators should slowly shrink homothetically, as well as translate. What interests us is the ‘second order’ changes to $L$ which cause this shrinking.

Far to the right in Figure 3.9, the LMCF translator $L$ approximates two non-intersecting affine Lagrangian planes $\tilde{\Pi}_{0},\tilde{\Pi}_{\boldsymbol{\phi}}$ in ${\mathbin{\mathbb{C}}}^{m}$ from (2.11), just as far to the right in Figure 2.1, the ‘grim reaper’ approximates two non-intersecting parallel lines in ${\mathbin{\mathbb{C}}}$. I suggest that to ‘second order’ in $L^{t}$, the two planes $\tilde{\Pi}_{0},\tilde{\Pi}_{\boldsymbol{\phi}}$ should be bent towards each other by a small angle, introducing a new immersed self-intersection point, and so that the noncompact $J$-holomorphic curve $\Sigma$ becomes a compact ‘teardrop’ as in Figure 2.3, which makes $HF^{*}$ obstructed. This modification $\tilde{L}$ of $L$ is sketched in Figure 3.10.

I expect that this ‘bending’ of $\tilde{\Pi}_{0},\tilde{\Pi}_{\boldsymbol{\phi}}$ towards one another is both the ‘outside influence’ in Principle 3.9(b) which makes $L$ shrink and causes the finite time singularity, and also the cause of the self-intersection point, the ‘teardrop’ curve $\Sigma$, and the obstructions to $HF^{*}$.