Results are obtained for two minimization problems: Ik(c) = inf{λk(Ω) : Ω open, convex in Rm, T (Ω) = c} and Jk(c) = inf{λk(Ω) : Ω quasi-open in Rm, |Ω| <= 1, P(Ω) <= c}, where c > 0, λk(Ω) is the kth eigenvalue of the Dirichlet Laplacian acting in L2(Ω), |Ω| denotes the Lebesgue measure of Ω, P(Ω) denotes the perime…