Generalized Symplectic Mean Curvature Flows in Almost Einstein Surfaces

• Published in: Chinese annals of mathematics. Serie B Vol. 35; no. 1; pp. 33 - 50
• Main Authors: Li, Jiayu, Yang, Liuqing
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 2014; Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China%Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China; School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, China
• Subjects: Applications of Mathematics; Mathematics; Mathematics and Statistics; 平均曲率流; 广义; 收敛性; 整体存在性; 无穷远; 爱因斯坦; 表面; 证明; Singularity; Almost Einstein; Symplectic mean curvature flow; Minimal surface; 53C44; 53C21
• ISSN: 0252-9599; 1860-6261
• DOI: 10.1007/s11401-013-0817-5

The authors mainly study the generalized symplectic mean curvature flow in an almost Einstein surface, and prove that this flow has no type-I singularity. In the graph case, the global existence and convergence of the flow at infinity to a minimal surface with metric of the ambient space conformal to the original one are also proved.