Mean Curvature Flow of Surfaces in Einstein Four-Manifolds
Mean Curvature Flow of Surfaces in Einstein Four-Manifolds
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DOI：
10.4310/jdg/1090348113
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发表时间：
2001-02
影响因子：
2.5
通讯作者：
Mu-Tao Wang
中科院分区：
文献类型：
--
作者：
Mu-Tao Wang
设M是四维KahlerEinstein流形（M，ω）中的紧致定向曲面.我们考虑的演变方向上的平均曲率向量的。证明了该流动沿着方向保持辛性，且不发生Ⅰ型奇点。当M有两个确定不同方向的平行Kahler形式ω′和ω′′，且M关于ω′和ω′′是辛的时，我们证明了M的平均曲率流始终光滑存在.在正曲率的情况下，流动确实在无穷远处收敛。
Let Σ be a compact oriented surface immersed in a four dimensional KahlerEinstein manifold (M,ω). We consider the evolution of Σ in the direction of its mean curvature vector. It is proved that being symplectic is preserved along the flow and the flow does not develop type I singularity. When M has two parallel Kahler forms ω′ and ω′′ that determine different orientations and Σ is symplectic with respect to both ω′ and ω′′, we prove the mean curvature flow of Σ exists smoothly for all time. In the positive curvature case, the flow indeed converges at infinity.