Singularities of codimension two mean curvature flow of symplectic surfaces

2002/08/29 by Jingyi Chen, Jiayu Li, Chen, Jingyi +1
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG

paper · pdf · doi:10.48550/arxiv.math/0208227

27 pages

arxiv created 2002/08/29 · openalex publication_date 2002/08/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that for a mean curvature flow of a compact symplectic surface in a compact Kaehler-Einstein surface, the tangent cone at the first blow-up time consists of a finite union of more than two 2-planes in R⁴ which are complex in a complex structure on R⁴.

Citations

• Convexity estimates for mean curvature flow and singularities of mean convex surfaces
• Calibrated geometries

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• The second type singularity of symplectic and Lagrangian mean curvature flows
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• A Characterization of the Singular Time of the Mean Curvature Flow