Ancient solutions and translators of Lagrangian mean curvature flow

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.

28 pages, v2: appendix added on smoothly immersed Brakke flows, accepted in Publ. Math. IHES

References in corpus (2)

• Uniqueness of convex ancient solutions to mean curvature flow in higher dimensions
• Singularities of Lagrangian mean curvature flow: zero-Maslov class case