Finite jet determination of CR embeddings (Q1769157)

The authors show that, under suitable conditions on the degeneracy of the maps and non-degeneracy of the manifolds, a CR embedding of a smooth CR hypersurface \(M\) of \(\mathbb{C}^N\) into another CR hypersurface \(\widehat{M}\subset\mathbb{C}^{\widehat{N}}\) is locally determined by its jet, of a given finite order, at a point. As an application, they obtain a reflection principle for CR maps between Levi-nondegenerate hypersurfaces in \(\mathbb{C}^N\) and \(\mathbb{C}^{N+1}\). They also give an independent proof of a result of \textit{F. Forsnerič} [Invent. Math. 95, No. 1, 31--62 (1989; Zbl 0633.32017)] on the reflection principle for maps between strictly pseudoconvex hypersurfaces in any codimension.