Annali di Matematica Pura ed Applicata

, Volume 173, Issue 1, pp 333–349 | Cite as

On the defect of an analytic disc

  • Patrizia Rossi


Although the concept of defect of an analytic disc attached to a generic manifold of Cn seems to play a merely technical role, it turns out to be a rather deep and fruitful notion for the extendability of CR functions defined on the manifold. In this paper we give a new geometric description of defect, drawing attention to the behaviour of the interior points of the disc by infinitesimal perturbations. For hypersurfaces a stronger result holds because these perturbations describe a complex vector space of Cn. For a big analytic disc the defect does not need to be smaller than the codimension of the manifold. Indeed we show by an example that it can be arbitrarily large independently of the codimension of the manifold. Nevertheless we also prove that the defect is always finite. In the case of a hypersurface we give a geometric upper bound for the defect.


Vector Space Interior Point Complex Vector Strong Result Geometric Description 
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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1997

Authors and Affiliations

  • Patrizia Rossi
    • 1
  1. 1.Dipartimento di MatematicaUniversità di Roma «Tor Vergata»RomaItaly

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