Work

The Bézout inequality for mixed volumes characterizes simplices

Year: 2026

Type: preprint

Abstract: We prove that the Bézout inequality for mixed volumes characterizes simplices among full dimensional convex bodies in every dimension, resolving a conjecture of Soprunov and Zvavitch. We give two separate proofs of the conjecture. Along the way, we also prove characterizations of simplices in terms of longest chords or relative inradii.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.20380

Authors: Langharst, Dylan, Wang, Shouda

Institutions: Carnegie Mellon University, KTH Royal Institute of Technology

Topic: Point processes and geometric inequalities

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Universität Bremen

Award: Postdoctoral Fellowship: MSPRF: On the Use of the Gaussian Measure in Convex Geometry

OpenAlex ID: W7213598640

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