Ebenfelt–Huang analyticity conjecture for CR-diffeomorphisms

Let $M,M'\subset\mathbb{C}^{2}$ be real-analytic Levi nonflat hypersurfaces. A $C^{\infty}$-smooth CR (local) diffeomorphism $F:M\to M'$ is a smooth CR map between such hypersurfaces.

Ebenfelt–Huang analyticity conjecture. Any $C^{\infty}$-smooth CR (local) diffeomorphism

$$F:M\to M'$$

extends holomorphically to an open neighborhood of $M$ in $\mathbb{C}^{2}$.

The conjecture addresses whether smooth CR-diffeomorphisms between real-analytic Levi nonflat hypersurfaces must be restrictions of holomorphic maps. Prior results established analyticity under additional assumptions, while the general question remained open even in dimension two.