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arXiv · 1107.0829

Long time existence of the symplectic mean curvature flow

Xiaoli Han·Jiayu Li
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Abstract

Let $(M,\bar{g})$ be a Kähler surface with a constant holomorphic sectional curvature $k>0$, and $Σ$ an immersed symplectic surface in $M$. Suppose $Σ$ evolves along the mean curvature flow in $M$. In this paper, we show that the symplectic mean curvature flow exists for long time and converges to a holomorphic curve if the initial surface satisfies $|A|^2\leq 2/3|H|^2+1/2 k$ and $\cosα\geq \frac{\sqrt{30}}{6}$ or $|A|^2\leq 2/3 |H|^2+4/5 k\cosα$ and $\cosα\ge251/265$.

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Xiaoli Han, Jiayu Li. 2011-07-05. Long time existence of the symplectic mean curvature flow. https://arxiv.org/abs/1107.0829

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