For the clamped plate on rectangles of fixed area, the first eigenvalue has a minimizer with aspect ratio below 1.066459, and the k-th minimizing rectangle tends to the square as k grows.
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Extremal eigenvalues of the Dirichlet biharmonic operator on rectangles
For the clamped plate on rectangles of fixed area, the first eigenvalue has a minimizer with aspect ratio below 1.066459, and the k-th minimizing rectangle tends to the square as k grows.