In this talk we will consider a reverse Faber-Krahn inequality for the principal eigenvalue μ_1(Ω) of the fully nonlinear operator P_{+N}u:=λ_N(D2u), where Ω⊂R^N is a bounded, open convex set, and λ_N(D^2u) is the largest eigenvalue of the Hessian matrix of u. The result will be a consequence of the isoperimetric inequality μ_1(Ω)≤π^2diam(Ω)^2. Moreover, we will discuss the minimization of μ1 under various kinds of constraints. The results have been obtained in collaboration with Julio D. Rossi and Ariel Salort (Buenos Aires).