On the analyticity of smooth CR maps into a real algebraic set
Let \(f: M \to M'\) be a \(C^\infty\)-smooth CR mapping between a generic real-analytic submanifold \(M\subset\mathbb C^n\) \((n\geqslant 2)\) and a real-algebraic subset \(M'\subset\mathbb C^{n'}\). The authors study the analyticity of such \(f\) and establish an upper bound for the transcendency degree of \(f\) as a function of the maximal dimension of local holomorphic foliation contained in \(M'\). It is proved that if \(M\) is minimal at a point \(p\) in the sense of Tumanov and if \(M'\) does not contain an open piece of complex curve, then \(f\) is real-analytic at \(p\).
scientific article; zbMATH DE number 1777397