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Ancient solutions and translators of Lagrangian mean curvature flow

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arxiv 2204.13836 v2 pith:XOGQKS7S submitted 2022-04-29 math.DG

classification math.DG
keywords lagrangianancientcurvatureflowmathcalmeanalmostcalibrated
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abstract

Suppose that $\mathcal{M}$ is an almost calibrated, exact, ancient solution of Lagrangian mean curvature flow in $\mathbb{C}^n$. We show that if $\mathcal{M}$ has a blow-down given by the static union of two Lagrangian subspaces with distinct Lagrangian angles that intersect along a line, then $\mathcal{M}$ is a translator. In particular in $\mathbb{C}^2$, all almost calibrated, exact, ancient solutions of Lagrangian mean curvature flow with entropy less than 3 are special Lagrangian, a union of planes, or translators.

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