2001/07/02 by P. Ebenfelt, Ebenfelt, P., B. Lamel +3 · 3 citations
Mathematics · #32H12 #32V20 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:32H12 #msc:32V20
paper · pdf · doi:10.48550/arxiv.math/0107013
arxiv created 2001/07/02 · arxiv updated 2009/11/30
We show that germs of local real-analytic CR automorphisms of a real-analytic hypersurface M in \C2 at a point p∈ M are uniquely determined by their jets of some finite order at p if and only if M is not Levi-flat near p. This seems to be the first necessary and sufficient result on finite jet determination and the first result of this kind in the infinite type case. If M is of finite type at p, we prove a stronger assertion: the local real-analytic CR automorphisms of M fixing p are analytically parametrized (and hence uniquely determined) by their 2-jets at p. This result is optimal since the automorphisms of the unit sphere are not determined by their 1-jets at a point of the sphere.