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Finite jet determination of local analytic CR automorphisms and their parametrization by 2-jets in the finite type case

P. Ebenfelt·B. Lamel·D. Zaitsev
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Abstract

We show that germs of local real-analytic CR automorphisms of a real-analytic hypersurface $M$ in $\C^2$ at a point $p\in M$ 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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P. Ebenfelt, B. Lamel, D. Zaitsev. 2001-07-02. Finite jet determination of local analytic CR automorphisms and their parametrization by 2-jets in the finite type case. https://arxiv.org/abs/math/0107013

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