English

Ancient solutions and translators of Lagrangian mean curvature flow

Differential Geometry 2024-01-22 v2

Abstract

Suppose that M\mathcal{M} is an almost calibrated, exact, ancient solution of Lagrangian mean curvature flow in Cn\mathbb{C}^n. We show that if M\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 M\mathcal{M} is a translator. In particular in C2\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.

Keywords

Cite

@article{arxiv.2204.13836,
  title  = {Ancient solutions and translators of Lagrangian mean curvature flow},
  author = {Jason D. Lotay and Felix Schulze and Gábor Székelyhidi},
  journal= {arXiv preprint arXiv:2204.13836},
  year   = {2024}
}

Comments

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