Extension of CR homeomorphisms between rigid polynomial varities (Q1860934)

Let \(f:M\longrightarrow M'\) be a CR-homeomorphism of two polynomial varieties of \(\mathbb C^n\). Assume that \(M\) and \(M'\) are minimal, rigid, and without nontrivial holomorphic curves. The author shows that \(f\) extends biholomorphically to a neighborhood of \(M\) in each of the following three cases: (1) \(f\) extends holomorphically to a neighborhood of a point \(p_0\in M\); (2) \(f\) is of class \(\mathcal C^1\); (3) \(M\) and \(M'\) are algebraic hypersurfaces.