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- Title
On the structure of pseudo-holomorphic discs with totally real boundary conditions.
- Authors
Oh, Yong-Geun
- Abstract
In this paper, we study the structure of J-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 any J-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 of J-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.
- Publication
Journal of Geometric Analysis, 1997, Vol 7, Issue 2, p305
- ISSN
1050-6926
- Publication type
Article
- DOI
10.1007/BF02921725