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arXiv · 1901.05383

Ancient solutions in Lagrangian mean curvature flow

Ben Lambert·Jason D. Lotay·Felix Schulze
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Abstract

Ancient solutions of Lagrangian mean curvature flow in C^n naturally arise as Type II blow-ups. In this extended note we give structural and classification results for such ancient solutions in terms of their blow-down and, motivated by the Thomas-Yau Conjecture, focus on the almost calibrated case. In particular, we classify Type II blow-ups of almost calibrated Lagrangian mean curvature flow when the blow-down is a pair of transverse planes or, when n=2, a multiplicity two plane. We also show that the Harvey-Lawson Clifford torus cone in C^3 cannot arise as the blow-down of an almost calibrated Type II blow-up.

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Ben Lambert, Jason D. Lotay, Felix Schulze. 2019-01-16. Ancient solutions in Lagrangian mean curvature flow. https://arxiv.org/abs/1901.05383

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