Abstract
We prove regularity, global existence, and convergence of Lagrangian mean curvature flows in the two-convex case (1.6). Such results were previously only known in the convex case, of which the current work represents a significant improvement. The proof relies on a newly discovered monotone quantity (2.6) that controls two-convexity. Through a unitary transformation, same result for the mean curvature flow of area-decreasing Lagrangian submanifolds (1.10) were established.
Funding Statement
C.-J. Tsai is supported by NSTC grant 110-2636-M-002-007, 111-2636-M-002-022, 112-2636-M-002-003 and NCTS.
M.-P. Tsui is supported by NSTC grant 109-2115-M-002-006. This material is based upon work supported by the National Science Foundation under Grant Numbers DMS-1810856 and DMS-2104212 (Mu-TaoWang).
Part of this work was carried out when M.-T. Wang was visiting the National Center of Theoretical Sciences.
Citation
Chung-Jun Tsai. Mao-Pei Tsui. Mu-Tao Wang. "Mean curvature flows of two-convex Lagrangians." J. Differential Geom. 128 (3) 1269 - 1284, November 2024. https://doi.org/10.4310/jdg/1729092459
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