ScalingStacks

Remark 3.10 . [03NZ]

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Remark 3.10.

(i) We will describe examples of behaviours (a),(b) in §3.5 and §3.8. Section 3.7 discusses a class of singularities not of type (a) or (b).

Note that in (a),(b) we do not simply mean that the singularity has a type II blow up {L~s:s∈ℝ}\{\tilde{L}^{s}:s\in{\mathbin{\mathbb{R}}}\} in Theorem 2.12 with L~s\tilde{L}^{s} special Lagrangian or an LMCF translator. In general type II blow ups describe only a small part of the singularity, and may give little idea of the global geometry and topology near the singular point. The point of (a),(b) is that in these cases we have a more complete picture of the singularity than a general type II blow up gives.

(ii) As in §2.3, Lagrangian MCF shrinkers do not occur in the graded case. The other major class of Lagrangian MCF solitons, Lagrangian MCF expanders (as in §2.3) are not relevant to the formation of singularities of the flow (that is, to describing the flow immediately before the singular time t=Tit=T_{i}). However, we can use Lagrangian MCF expanders to model the flow immediately after a surgery at a singular time t=Tit=T_{i}, and we do this in §3.4.

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