# Jet determination of smooth CR automorphisms and generalized stationary discs

## TL;DR

This paper establishes finite jet determination for smooth CR diffeomorphisms of Levi degenerate hypersurfaces in complex space by constructing specialized stationary discs.

## Contribution

It introduces a method using generalized stationary discs to prove finite jet determination for smooth CR automorphisms on Levi degenerate hypersurfaces.

## Key findings

- Finite jet determination holds for smooth CR diffeomorphisms.
- Construction of generalized stationary discs glued to hypersurfaces.
- Applicable to Levi degenerate hypersurfaces in complex space.

## Abstract

We prove finite jet determination for (finitely) smooth CR diffeomorphisms of (finitely) smooth Levi degenerate hypersurfaces in $\mathbb{C}^{n+1}$ by constructing generalized stationary discs glued to such hypersurfaces.