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Unique determination of local CR-maps by their jets: a survey. (English) Zbl 1098.32018
The paper under review is a survey on the unique determination of local CR automorphisms, of which a significative sample is the following result, due to P. Ebenfelt, B. Lamel and D. Zaitsev [Finite jet determination of local analytic CR automorphisms and their parametrization by \(2\)-jets in the finite type case, preprint, 2001, http://arXiv.org/abs/math.CV/0107013, see also J. Geom. Anal. 14, No. 2, 241–265 (2004; Zbl 1076.32023)]: local biholomorphisms of a \(C^\omega\) real hypersurface \(M \subset \mathbb C^2\) at a point \(p \in M\) are uniquely determined by their \(k\)-jets for some \(k\) if and only if \(M\) is not Levi-flat (near \(p\)). No proofs are given.Zbl 1076.32023

32V10 CR functions