On the structure of pseudo-holomorphic discs with totally real boundary conditions
On the structure of pseudo-holomorphic discs with totally real boundary conditions
复制标题
全实边界条件赝全纯圆盘的结构研究
DOI：
10.1007/bf02921725
复制
发表时间：
1997
期刊：
影响因子：
--
通讯作者：
Y. Oh
中科院分区：
文献类型：
--
作者：
Y. Oh
本文研究了几乎复流形（M，J）中J-全纯圆的结构，它与具有全真实的边界条件的伪全纯圆的Fredholm理论有关.我们证明了任何具有全真实的边界条件的J-全纯圆盘，除了在一个离散的点集上是内射的，我们称之为“正规圆盘”，它必须要么有一个正则的重数为1的边界点，要么满足它的像形成一个光滑的浸入紧致曲面（无边界），有有限个自相交点和有限个分支点.在证明这一定理的过程中，我们还证明了J-全纯圆盘边界点的局部结构的几个定理，作为应用，我们给出了辛几何中关于Lagrange交的Floer伪全纯轨线的横截性结果的完整处理。
In this paper, we study the structure ofJ-holomorphic discs in relation to the Fredholm theory of pseudo-holomorphic discs with totally real boundary conditions in almost complex manifolds (M, J). We prove that anyJ-holomorphic disc with totally real boundary condition that is injective in the interior except at a discrete set of points, which we call a “normalized disc,” must either have some boundary point that is regular and has multiplicity one, or satisfy that its image forms a smooth immersed compact surface (without boundary) with a finite number of self-intersections and a finite number of branch points. In the course of proving this theorem, we also prove several theorems on the local structure of boundary points ofJ-holomorphic discs, and as an application we give a complete treatment of the transverslity result for Floer’s pseudo-holomorphic trajectories for Lagrangian intersections in symplectic geometry.