Symplectic mean curvature flow in CP
2 |
| |
Authors: | Xiaoli Han Jiayu Li Liuqing Yang |
| |
Institution: | 1. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, People’s Republic of China 2. School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, People’s Republic of China 3. Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing, 100190, People’s Republic of China
|
| |
Abstract: | Let Σ be an immersed symplectic surface in CP 2 with constant holomorphic sectional curvature k > 0. Suppose Σ evolves along the mean curvature flow in CP 2. 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 ${|A|^2 \leq \lambda|H|^2 + \frac{2\lambda-1}{\lambda}k}$ and ${\cos\alpha\geq\sqrt{\frac{7\lambda-3}{3\lambda}}\left(\frac{1}{2} < \lambda\leq\frac{2}{3}\right) {\rm or} |A|^2\leq \frac{2}{3}|H|^2+\frac{4}{5}k\cos\alpha\, {\rm and} \cos\alpha\geq 1-\varepsilon}$ , for some ${\varepsilon}$ . |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|