As on arXiv
Abstract
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.
Comments: typos corrected; small changes reflecting referee comments; to appear in J. Differential Geom
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The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2021, plus the canon.
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Entire solutions of two-convex Lagrangian mean curvature flows
Topics Lagrangian mean curvature flow, Long-time existence & convergence · Same authors Chung-Jun Tsai, Mao-Pei Tsui, Mu-Tao Wang · Shared terms “convex lagrangian”, “Lagrangian submanifold”, “previously”
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Almost isoclinic Lagrangian submanifolds
Topics Lagrangian mean curvature flow · Same author Mu-Tao Wang · Shared terms “Lagrangian submanifold”
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Infinite-Time Singularities with Vanishing Mean Curvature for Lagrangian Mean Curvature Flow in Gibbons–Hawking Spaces
Topics Lagrangian mean curvature flow · Same author Chung-Jun Tsai
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A New Monotone Quantity in Mean Curvature Flow Implying Sharp Homotopic Criteria
Topics Mean curvature flow · Same authors Chung-Jun Tsai, Mao-Pei Tsui, Mu-Tao Wang · Shared terms “monotone quantities”, “area decreasing”, “submanifolds”
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Infinite-Time Singularities of the Lagrangian Mean Curvature Flow
Topics Lagrangian mean curvature flow · Same author Chung-Jun Tsai
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Lagrangian mean curvature flow in the Kummer K3 surface
Topics Lagrangian mean curvature flow, Long-time existence & convergence
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Dynamical Stability of Minimal Lagrangians in Kähler-Einstein Manifolds of Non-Positive Curvature
Topics Lagrangian mean curvature flow · Same author Chung-Jun Tsai
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Lagrangian mean curvature flow of surfaces with mean curvature bound
Topics Lagrangian mean curvature flow
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- 6A.10Curve Shortening and the First Geometric Flows
Shrinking circles, grim reapers, neckpinches and Huisken’s monotonicity, seen in the plane.