For fully nonlinear $k$-Hessian operators on bounded strictly $(k-1)$-convex domains $\Omega$ of $\mathbb{R}^N$, a characterization the principal eigenvalue associated to $k$-convex and negative eigenfunction will be given as supremum over values spectral parameter for which admissible viscosity supersolutions obey minimum principle. The admissibility condition is phrased in terms natura...
