Journal d’Analyse Mathematique

, Volume 72, Issue 1, pp 261–278

Regularity of discs attached to a submanifold ofCn


    • Department of MathematicsUniversity of Ljubljana

DOI: 10.1007/BF02843161

Cite this article as:
Cerne, M. J. Anal. Math. (1997) 72: 261. doi:10.1007/BF02843161


Letp be an analytic disc attached to a generating CR-submanifoldM of Cn. It is proved that some recently introduced conditions onp andM which imply that the family of all smallCα holomorphic perturbations ofp alongM is a Banach submanifold of (Aα(D))n are equivalent. These conditions are given in terms of the partial indices of the discp attached toM and “holomorphic sections” of the conormal bundle ofM along p(∂D). Also, a sufficient geometric conditionon p andM is given so that the family of all smallCα holomorphic perturbationsof p alongM, fixed at some boundary point, is a Banach submanifold of (Aα (D))n.

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© Hebrew University 1997