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Ancient solutions and translators of Lagrangian mean curvature flow

  • Jason D. Lotay,
  • Felix Schulze,
  • Gábor Székelyhidi

摘要

Suppose that ℳ is an almost calibrated, exact, ancient solution of Lagrangian mean curvature flow in C n $\mathbf {C} ^{n}$ . 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 C 2 $\mathbf {C} ^{2}$ , 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.