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arXiv · 2610.06806

Higher-order Godbersen inequality and a characterization of simplices via the face lattice

Filip Fryš·Jan Kotrbatý·Mohamed A. Mouamine·Shouda Wang
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Abstract

We settle the long-standing Godbersen conjecture that the mixed volume of a convex body of fixed positive volume with its reflection about the origin is maximized precisely by simplices. For the proof, we establish a new characterization of simplices by a natural incidence relation on the face lattice. Moreover, we establish a higher-order generalization of the Godbersen inequality and show that simplices are the only nontrivial equality cases, confirming a conjecture of Schneider from 2000.

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Filip Fryš, Jan Kotrbatý, Mohamed A. Mouamine, Shouda Wang. 2026-10-05. Higher-order Godbersen inequality and a characterization of simplices via the face lattice. https://arxiv.org/abs/2610.06806

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