Ebenfelt, P.; Lamel, B.; Zaitsev, D. 'Finite jet determination of local analytic CR automorphisms and their parametrization by 2-jets in the finite type case' in Geometric And Functional Analysis, 13, (3), 2003, pp 546 - 573
Geometric And Functional Analysis 13 3
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.
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