Mean Curvature Flows of Two-Convex Lagrangians

We prove regularity, global existence, and convergence of Lagrangian mean curvature flows in the two-convex case. 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 that...

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Bibliographic Details
Published inarXiv.org
Main Authors Chung-Jun, Tsai, Mao-Pei Tsui, Mu-Tao, Wang
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 21.12.2023
Subjects
Convexity
Curvature
Manifolds (mathematics)
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Summary:We prove regularity, global existence, and convergence of Lagrangian mean curvature flows in the two-convex case. 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 that controls two-convexity. Through a unitary transformation, same result for the mean curvature flow of area-decreasing Lagrangian submanifolds were established.
ISSN:2331-8422