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We consider a representation of a finitely generated CAT(--K) group $\Gamma$in SL(d, R) that is Zariski dense and k-Anosov for at least two values of k. Weexhibit a gap for the Minkowski dimension of minimal sets for the action of$\Gamma$ on flags spaces. The proof uses a variational principle for the actionon partial flags.

Dimension gap and variational principle for Anosov representations