Ancient solutions and translators of Lagrangian mean curvature flow

Abstract

AbstractSuppose that ℳ is an almost calibrated, exact, ancient solution of Lagrangian mean curvature flow in $\mathbf {C} ^{n}$ C n . We show that if ℳ has a blow-down given by the static union of two Lagrangian subspaces with distinct Lagrangian angles that intersect along a line, then ℳ is a translator. In particular in $\mathbf {C} ^{2}$ 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.