Local automorphisms and mappings of smooth strictly pseudoconvex hypersurfaces

Suppose given a smooth strictly pseudoconvex hypersurface not equivalent to the sphere, a point on the surface, and a neighborhood of the point. It is shown that all local automorphisms of the surface defined in an arbitrary neighborhood of a fixed point can be linearized by a suitable choice of local coordinates. It is also shown that given two convergent sequences of real analytic nonspherical hypersurfaces it is possible to extract a convergent subsequence from any sequence of mappings between them.
Bibliography: 20 titles.