Abstract
Suppose that ℳ is an almost calibrated, exact, ancient solution of Lagrangian mean curvature flow in \(\mathbf {C} ^{n}\). 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 \(\mathbf {C} ^{2}\), 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.
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Acknowledgements
This project grew out of discussions at the AIM workshop “Stability in mirror symmetry” in December 2020. We are grateful to the referees for many helpful suggestions which improved the exposition of the paper.
Funding
JDL and FS were partially supported by a Leverhulme Trust Research Project Grant RPG-2016-174. GSz was supported in part by NSF grant DMS-1906216.
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Lotay, J.D., Schulze, F. & Székelyhidi, G. Ancient solutions and translators of Lagrangian mean curvature flow. Publ.math.IHES (2024). https://doi.org/10.1007/s10240-023-00143-5
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DOI: https://doi.org/10.1007/s10240-023-00143-5