The deformation of symplectic critical surfaces in a Kahler surface-II-compactness

作者：Han, Xiaoli; Li, Jiayu; Sun, Jun^*

来源：Calculus of Variations and Partial Differential Equations, 2017, 56(3): 84.

DOI：10.1007/s00526-017-1175-z

• MINIMAL-SURFACES
• RICCI CURVATURE
• SUBMANIFOLDS
• MANIFOLD
• SPACE

In this paper we consider the compactness of beta-symplectic critical surfaces in a Kahler surface. Let M be a compact Kahler surface and Sigma(i) subset of M be a sequence of closed beta(i)-symplectic critical surfaces with beta(i) -> beta(0) is an element of (0, infinity). Suppose the quantity integral Sigma(i)1/cos(q) alpha(i) d mu(i) (for some q > 4) and the genus of Sigma(i) are bounded, then there exists a finite set of points S subset of M and a subsequence Sigma(i)' which converges uniformly in the C-l topology (for any l < 8) on compact subsets of M\S to a beta(0)-symplectic critical surface Sigma subset of M, each connected component of Sigma\S can be extended smoothly across S.

• 出版日期2017-6
• 单位中国科学技术大学; 武汉大学; 中国科学院数学与系统科学研究院; 清华大学