arXiv (OAI Expanded)
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Godbersen's conjecture and the $L_p$-Rogers-Shephard inequality
We prove that the mixed volume of a convex body of fixed positive volume with its reflection about the origin is maximized by simplices. This confirms a conjecture of C. Godbersen from 1938 and refines the classical Rogers-Shephard inequality. We also prove that simplices are the only extremizers am
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