Work

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

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.06806

Authors: Fryš, Filip, Kotrbatý, Jan, Mouamine, Mohamed A., Wang, Shouda

Language: English

Topic: Point processes and geometric inequalities

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Univerzita Karlova v Praze, Knut och Alice Wallenbergs Stiftelse

Awards: G5362880987, G6203253224

OpenAlex ID: W7220648380

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