Stationary holomorphic discs and finite jet determination problems

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.