On the regularity of the Green current for semi-extremal endomorphisms of \begin{document}$ \mathbb{P}^2 $\end{document}

We study the regularity of the Green current for semi-extremal endomorphisms of \begin{document}$ \mathbb{P}^2 $\end{document} . Under suitable assumptions, we show that the pointwise lower Radon-Nikodym derivative of stable slices with respect to the one dimensional Lebesgue measure is bounded at almost every point for the equilibrium measure. This provides a weak amount of metric regularity for the Green current along holomorphic discs.