Godbersen’s conjecture for locally anti-blocking bodies
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Shay Sadovsky
Abstract
In this note we give a short proof of Godbersen’s conjecture for the special class of locally anti-blocking bodies. We show that all equality cases amongst locally anti-blocking bodies are for locally anti-blocking simplices, further supporting the conjecture. The proof of the equality cases introduces a useful calculation of mixed volumes of aligned simplices.
Funding statement: This research was partially supported by ISF Grant No. 784/20. The author is also grateful to the Azrieli foundation for the award of an Azrieli fellowship.
Acknowledgements
The author would like to thank Shiri Artstein-Avidan, for her supervision and guidance, and Arnon Chor, for many insightful discussions and his thorough reading of this manuscript. The author thanks Raman Sanyal for pointing out the second proof of Lemma 1.2, and Martin Henk for bringing the references [13; 20] to her attention.
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Communicated by: F. Santos
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Articles in the same Issue
- Frontmatter
- Combinatorics of stratified hyperbolic slices
- Godbersen’s conjecture for locally anti-blocking bodies
- A Hilbert metric for bounded symmetric domains
- On the generalized Suzuki curve
- The partition of PG(2, q3) arising from an order 3 planar collineation
- Well-rounded lattices from odd prime degree number fields in the ramified case
- Split Cayley hexagons via subalgebras of octonion algebras
- Relative Lipschitz saturation of complex algebraic varieties
- The prime grid contains arbitrarily large empty polygons
- The geometry of locally bounded rational functions
Articles in the same Issue
- Frontmatter
- Combinatorics of stratified hyperbolic slices
- Godbersen’s conjecture for locally anti-blocking bodies
- A Hilbert metric for bounded symmetric domains
- On the generalized Suzuki curve
- The partition of PG(2, q3) arising from an order 3 planar collineation
- Well-rounded lattices from odd prime degree number fields in the ramified case
- Split Cayley hexagons via subalgebras of octonion algebras
- Relative Lipschitz saturation of complex algebraic varieties
- The prime grid contains arbitrarily large empty polygons
- The geometry of locally bounded rational functions
