Pseudoholomorphic Discs Attached to Pseudoconcave Domains

  • Luca Baracco
  • Anna Siano
  • Giuseppe Zampieri
Conference paper
Part of the Trends in Mathematics book series (TM)


We discuss almost complex perturbations of linear discs. We give precise estimates for the (1, α) norm of these deformations and for the dependence on parameters. In particular, we show how families of such discs give rise to local foliations of the space. Also, if Ω is a domain whose boundary is endowed with at least one negative eigenvector w 1 at 0 for the standard structure of ℂn, then small discs with velocity w 1 which are analytic for a C 1-perturbation of the structure, have boundary which is contained in ? in a neighborhood of 0. In particular, if the almost complex structure is real analytic, almost holomorphic functions extend along the corresponding foliation of discs.


Holomorphic Function Levi Form Standard Structure Analytic Disc Standard Disc 
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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2006

Authors and Affiliations

  • Luca Baracco
    • 1
  • Anna Siano
    • 1
  • Giuseppe Zampieri
    • 1
  1. 1.Dipartimento di MatematicaUniversità di PadovaPadovaItaly

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