Principle 3.18 . [03PA]
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Principle 3.18.
(a) In the programme of §3.2, in dimension for the Lagrangians at nonsingular times we should allow Lagrangians with ‘stable special Lagrangian singularities’. These should include stable isolated conical singularities, as in [33], and probably also other classes of non-isolated or non-conical singularities.
For example, if with and is a stable special Lagrangian cone in as above, the author expects that Lagrangians with -dimensional singularities locally modelled on in are ‘stable’.
In dimension Lagrangians with conical singularities modelled on the -cone in (2.4) may be the only kind required. As increases, the singularities allowed will probably become more and more complicated.
(b) For each such class of stable singularities one should prove short time existence for Lagrangian MCF.
(c) One should extend the definitions of Lagrangian Floer cohomology, obstructions to and to include each such class of stable singularities.