Singularities of symplectic and Lagrangian mean curvature flows

2006/11/28 by Xiaoli Han, Jiayu Li, Han, Xiaoli +1
Mathematics · #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.math/0611857

openalex publication_date 2006/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study the singularities of the mean curvature flow from a symplectic surface or from a Lagrangian surface in a Kähler-Einstein surface. We prove that the blow-up flow Σ_s^∞ at a singular point (X₀, T₀) of a symplectic mean curvature flow Σ_t or of a Lagrangian mean curvature flow Σ_t is a non trivial minimal surface in \bf R⁴, if Σ_-∞^∞ is connected.

Citations

• Differential equations on riemannian manifolds and their geometric applications
• Calibrated geometries

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