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Perturbing analytic discs attached to maximal real submanifolds of \(\mathbb{C}^ N\). (English) Zbl 0861.32013
Let \(f\) be an analytic disc in \(\mathbb{C}^N\) attached to a maximal real submanifold \(M\) of \(\mathbb{C}^N\). The author introduced in a recent paper [Math. Z. 217, No. 2, 287-316 (1994; Zbl 0806.58044)] partial indices \(k_j\), \(1\leq j\leq N\), of \(M\) along the boundary of \(f\) and showed that if \(k_j\geq 0\) for all \(j\) then the family of nearby analytic discs attached to \(M\) depends on \(k_1+ \cdots +k_N\) parameters. Y.-G. Oh sharpened this by proving the same when \(k_j\geq -1\) for all \(j\) and showed that in terms of stability this is the best possible condition. In the paper under review the author explains why the latter condition is natural and give a simple proof of Oh’s result in the orientable case.

MSC:
32G10 Deformations of submanifolds and subspaces
32V40 Real submanifolds in complex manifolds
32D10 Envelopes of holomorphy
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