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PreprintarXiv licencearXiv

The Bézout inequality for mixed volumes characterizes simplices

  • Dylan Langharst
  • Shouda Wang
Open at sourcePDFDOICite

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.

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Cite

BibTeXRIS
BibTeX
@misc{langharst2026bézout,
  title = {{The Bézout inequality for mixed volumes characterizes simplices}},
  author = {Dylan Langharst and Shouda Wang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.20380},
  eprint = {2609.20380},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.20380},
}
RIS
TY  - UNPB
TI  - The Bézout inequality for mixed volumes characterizes simplices
AU  - Dylan Langharst
AU  - Shouda Wang
PY  - 2026
DA  - 2026/09/17
PB  - arXiv
DO  - 10.48550/arxiv.2609.20380
UR  - https://arxiv.org/abs/2609.20380
AB  - 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.
ER  -