On maps between nonminimal hypersurfaces

We construct an analytic jet parametrization for nontrivial CR maps between real-analytic 1-nonminimal hypersurfaces in ${\mathbb{C}^2}$ . In particular, this gives a real-analytic structure on the set of all such maps, and shows that the automorphism groups of a 1-nonminimal hypersurface in ${\mathbb{C}^2}$ is a Lie group. Our results also hold for some classes of 1-nonminimal hypersurfaces in higher dimensions.