Weighted sums of the mixed volumes V(K[j],-K[n-j]) are bounded by Vol(K), sharp for simplices, giving an averaged Godbersen inequality and extending Rogers-Shephard.
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On unbalanced difference bodies and Godbersen's conjecture
Weighted sums of the mixed volumes V(K[j],-K[n-j]) are bounded by Vol(K), sharp for simplices, giving an averaged Godbersen inequality and extending Rogers-Shephard.