Author

Jan Kotrbatý

3 papers indexed here

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Preprint Oct 2026

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

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 est...

Filip Fryš, Jan Kotrbatý, Mohamed A. Mouamine et al. · 1 citation

Preprint Jul 2026

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 among convex polytopes...

Jan Kotrbatý, Mohamed A. Mouamine · 3 citations · ⚡2

Preprint Jul 2026

Godbersen's conjecture and the $L_p$-Rogers-Shephard inequality

We prove that the mixed volume of a convex body with its reflection about the origin is maximized by simplices. This confirms a conjecture of C. Godbersen from 1938 and refines the Rogers-Shephard inequality. We also prove that, among convex polytopes, simplices are the only extremizers. Finally, we use this inequality...

Jan Kotrbatý, Mohamed A. Mouamine · 1 citation · ⚡1