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We consider the minimization of Dirichlet eigenvalues    λ  k   ,    k  ∈  N   , of the Laplacian on cuboids of unit measure in    R  3   . We prove that any sequence of optimal cuboids in    R  3    converges to a cube of unit measure in the sense of Hausdorff as    k  →  ∞   . We also obtain an upper bound for that rate of convergence.

MINIMIZING DIRICHLET EIGENVALUES ON CUBOIDS OF UNIT MEASURE