Let (Rn, dX) be a Carnot–Carathéodory metric space generated by a family of smooth vector fields {Xi}i=1m satisfying Hörmander’s finite rank condition, and $\mathcal{H}_{X}=\{(x,\sum_{i=1}^{m}a_{i}X_{i}(x))|x\in\mathbf{R}^{n},(a_{i})_{i=1}^{m}\in\mathbf{R}^{m}\}$ be the horizontal tangent bundle generated by {Xi}i=1m. Assume that $H=H(x,p)\in C^{1}(\mathcal{H}_{X})$ is quasiconvex in p-variable. We prove that any absolute minimizer u∈WX1, ∞(Ω) to F∞(v, Ω)=ess supx∈ΩH(x, Xv(x)) is a viscosity solution of the Aronsson equation
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\[\mathcal{A}^{X}[u]:=X(H(x,Xu(x)))\cdot H_{p}(x,Xu(x))=0\quad\hbox{in }\Omega.\]