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Singularity formations in Lagrangian mean curvature flow
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We study singularities along the Lagrangian mean curvature flow with tangent flows given by multiplicity one special Lagrangian cones that are smooth away from the origin. Some results are: uniqueness of all such tangent flows in dimension two; uniqueness in any dimension when the link of the cone is connected; the existence of nontrivial special Lagrangian blowup limits. We also prove a singular version of Imagi-Joyce-dos Santos's uniqueness result of the Lawlor neck. As an application we prove that in any dimension, singularities that admit a tangent flow given by the union of two transverse planes is modeled on shrinking Lawlor necks at suitable scales.
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Cited by 1 Pith paper
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Finite-Time Singularities of Lagrangian Mean Curvature Flow with Quantitatively Precise Dynamics
Almost-calibrated cohomogeneity-one Lagrangian mean curvature flows in C^n develop Type II singularities with precise curvature rate (T-t)^{-K/2} for admissible K,n, with cone pair tangent flow and smooth desingulariz...
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