Fredholm-Regularity of Holomorphic Discs in Plane Bundles over Compact Surfaces

  title={Fredholm-Regularity of Holomorphic Discs in Plane Bundles over Compact Surfaces},
  author={Brendan Guilfoyle and Wilhelm Klingenberg},
  journal={arXiv: Analysis of PDEs},
We study the space of holomorphic discs with boundary on a surface in a real 2-dimensional vector bundle over a compact 2-manifold. We prove that, if the ambient 4-manifold admits a fibre-preserving transitive holomorphic action, then a section with a single complex point has $C^{2,\alpha}$-close sections such that any (non-multiply covered) holomorphic disc with boundary in these sections are Fredholm regular. Fredholm regularity is also established when the complex surface is neutral Kahler… 
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