Stationary Discs for Smooth Hypersurfaces of Finite Type and Finite Jet Determination

Abstract

We construct a finitely dimensional manifold of invariant holomorphic discs attached to a certain class of smooth pseudoconvex hypersurfaces of finite type, generalizing the notion of stationary discs. The discs we construct are determined by a finite jet at a given boundary point and their centers fill an open set. As a consequence, we obtain finite jet determination of CR diffeomorphisms between smooth hypersurfaces of this class.