Tangent Flows of Symplectic Mean Curvature Flows

Abstract

We prove that the tangent cone at the first blow-up time of the mean curvature flow of a closed symplectic surface in a compact Kahler-Einstein surface consists of a finite union of planes in R⁴. Furthermore, when the flow develops a Type I^* singularity at (X₀,T), then the tangent cone is a holomorphic cone.

Keywords

Symplectic mean curvature flow / tangent flow / Type I^* singularity / holomorphic curve

Acknowledgment

The second author is supported by National Key R&D Program of China (Grant No. 2022YFA1005400)and NFSC (Grant No. 12031017). The third author is supported by NFSC (Grant Nos. 12531002, 11721101 and 12031017). The fourth author is supported by NSFC (Grant Nos. 12071352, 12271039 and 12531002).

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