Variational approach to the asymptotic mean-value property for the p-Laplacian on Carnot groups

Let $1<p\le \mathrm{\infty }$. We provide an asymptotic characterization of continuous viscosity solutions $u$ of the normalized $p$-Laplacian ${\mathrm{\Delta }}_{p\mathbb{G}}^{N}u=0$ in any Carnot group $\mathbb{G}$.