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Inspired by work of McMullen, we show that any orbit for the action of thediagonal group on the space of lattices, accumulates on a stable lattice. Weuse this to settle a conjecture of Ramharter about Mordell's constant, get newproofs of Minkowski's conjecture in dimensions up to seven, and answer aquestion of Harder on the volume of stable lattices.

On stable lattices and the diagonal group