Local automorphisms and mappings of smooth strictly pseudoconvex hypersurfaces

N. G. Kruzhilin

Izvestiya. Mathematics , Tome 26 (1986) no. 3, pp. 531-552.

Résumé

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.

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