Self-similar solutions and translating solitons for Lagrangian mean\n curvature flow

2008/01/24 by Dominic Joyce, Joyce, Dominic, Yng-Ing Lee +3 · 3 citations
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.0801.3721

openalex publication_date 2008/01/24 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

We construct many self-similar and translating solitons for Lagrangian mean\ncurvature flow, including self-expanders and translating solitons with\narbitrarily small oscillation on the Lagrangian angle. Our translating solitons\nplay the same role as cigar solitons in Ricci flow, and are important in\nstudying the regularity of Lagrangian mean curvature flow.\n Given two transverse Lagrangian planes Rⁿ in Cⁿ with sum of characteristic\nangles less than pi, we show there exists a Lagrangian self-expander asymptotic\nto this pair of planes. The Maslov class of these self-expanders is zero. Thus\nthey can serve as local models for surgeries on Lagrangian mean curvature flow.\nFamilies of self-shrinkers and self-expanders with different topologies are\nalso constructed. This paper generalizes the work of Anciaux, Joyce, Lawlor,\nand Lee and Wang.\n

Cited by

• Relative Liouville Rigidity for Lagrangian Self-Similar Submanifolds with Legendrian Boundary
• Rigidity and Classification of Legendrian Self-Shrinkers
• Lagrangian Translating Solitons and Special Lagrangians in ℂ^m with Symmetries

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