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PreprintCC BY 4.0arXiv

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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Cite

BibTeXRIS
BibTeX
@misc{frys2026higherorder,
  title = {{Higher-order Godbersen inequality and a characterization of simplices via the face lattice}},
  author = {Filip Fryš and Jan Kotrbatý and Mohamed A. Mouamine and Shouda Wang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.06806},
  eprint = {2610.06806},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.06806},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Higher-order Godbersen inequality and a characterization of simplices via the face lattice
AU  - Filip Fryš
AU  - Jan Kotrbatý
AU  - Mohamed A. Mouamine
AU  - Shouda Wang
PY  - 2026
DA  - 2026/10/12
PB  - arXiv
DO  - 10.48550/arxiv.2610.06806
UR  - https://arxiv.org/abs/2610.06806
AB  - 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.
ER  -