Stationary holomorphic discs and finite jet determination problems

Abstract

We construct a family of small analytic discs attached to Levi non-degenerate hypersurfaces in ${\mathbb{C}}^{n+1}$, which is globally biholomorphically invariant. We then apply this technique to study unique determination problems along Levi non-degenerate hypersurfaces that are merely of class ${\mathcal{C}}^4$. This method gives 2-jet determination results for germs of biholomorphisms, CR diffeomorphisms, as well as in the almost complex setting.

23 pages