Answers to questions of Grünbaum and Loewner
We construct a convex body K in R n , n ≥ 5 , with the property that there is exactly one hyperplane H passing through c ( K ) , the centroid of K , such that the centroid of K ∩ H coincides with c ( K ) . This provides answers to questions of Grünbaum and Loewner for n ≥ 5 . The proof is based on the existence of non-intersection bodies in these dimensions.
Authors
- Vladyslav Yaskin (ORCID: https://orcid.org/0000-0001-9078-2672)
- Sergii Myroshnychenko (ORCID: https://orcid.org/0000-0003-0143-0275)
- Kateryna Tatarko (ORCID: https://orcid.org/0000-0001-8638-134X)
Institutions
- University of Waterloo (CA)
- University of Alberta (CA)
- University of the Fraser Valley (CA)
Publication Details
- Journal
- Advances in Mathematics
- Published
- 2024-12-16
- DOI
- https://doi.org/10.1016/j.aim.2024.110081
- Primary Topic
- Point processes and geometric inequalities
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Natural Sciences and Engineering Research Council of Canada