, Volume 72, Issue 1, pp 261-278

Regularity of discs attached to a submanifold ofC n

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Abstract

Letp be an analytic disc attached to a generating CR-submanifoldM of C n . It is proved that some recently introduced conditions onp andM which imply that the family of all smallC α 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 smallC α holomorphic perturbationsof p alongM, fixed at some boundary point, is a Banach submanifold of (A α (D))n.