On genericity for holomorphic curves in four-dimensional almost-complex manifolds
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We consider spaces of immersed (pseudo-)holomorphic curves in an almost complex manifold of dimension four. We assume that they are either closed or compact with boundary in a fixed totally real surface, so that the equation for these curves is elliptic and has a Fredholm index. We prove that this equation is regular if the Chern class is ≥ 1 (in the case with boundary, if the ambient Maslov number is ≥ 1). Then the spaces of holomorphic curves considered will be manifolds of dimension equal to the index.
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- On genericity for holomorphic curves in four-dimensional almost-complex manifolds
The Journal of Geometric Analysis
Volume 7, Issue 1 , pp 149-159
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- Holomorphic curve
- almost complex manifold
- nonlinear elliptic PDE
- Fredholm index
- Author Affiliations
- 1. Courant Institute, New-York University, 251 Mercer Street, 10012, New-York, NY, USA
- 2. U.F.R. Sciences, Mathématiques, I.U.F.M. de Toulouse, 118, route de Narbonne, F-31078, Toulouse cedex 4
- 3. Laboratoire Emile Picard, UMR CNRS 5578, Université Paul Sabatier, 118, route de Narbonne, F-31062, Toulouse