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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
##### Keywords:
analytic disc; maximal real submanifold
Full Text:
##### References:
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