Regularity of discs attached to a submanifold ofC ^{n} Article

Received: 01 December 1996 Revised: 01 July 1997 DOI :
10.1007/BF02843161

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

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Authors and Affiliations 1. Department of Mathematics University of Ljubljana Ljubljana Slovenia