= Solution
Since $\mathbf a\ne0$, the line $\mathbf x=t\mathbf a/\|\mathbf a\|^2$ lies in the domain and satisfies $\mathbf a^{\mathsf T}\mathbf x=t$. The restriction of $l$ to this line is $t^3$, whose second <derivative> is $6t$: negative for $t<0$ and positive for $t>0$. It can be neither globally <convex> nor globally <concave>. Hence \b[$l$ is neither]. Equivalently, its <Hessian matrix> is $6(\mathbf a^{\mathsf T}\mathbf x)\mathbf a\mathbf a^{\mathsf T}$, changing the sign of its nonzero directional curvature across $\mathbf a^{\mathsf T}\mathbf x=0$.
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