Some of the generic singularities in the LMCF are expected to have elliptic analogues in the continuity method approach. We fix $\omega$ and consider a generic 1-parameter family of $\Omega$, and we follow the Lagrangian flux zero deformations of a given special Lagrangian.

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  Under exact isotopy, immersed Lagrangians may lose the unobstructed condition. One expects the surgery of the brane structure suggested by Joyce has an elliptic analogue, involving the same ingredients as the ‘Maslov flow’ studied by Woodward and Palmer [81][82].

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  As already discussed in section 2.7, the Lawlor neck is responsible for the gluing of two immersed special Lagrangians. This corresponds to the ‘Lawlor neck pinching’ singularity, as well as the ‘openning the neck’ surgery in the LMCF.

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  (Stable singularity) Joyce suggests from his work on $U(1)$-invariant special Lagrangians in $\mathbb{C}^{3}$ [41, Example 2.8], that in a continuous 1-parameter family, isolated singular points of special Lagrangian 3-folds with local $T^{2}$-cone singularities can appear and disappear in pairs, by making the two $T^{2}$-cone singularities collide with each other and then smooth out. This is the main motivation for admitting the $T^{2}$-cone singularity in the LMCF, and it seems likely to be a generic singularity in the continuity method as well.