Small Volume Bodies of Constant Width
Abstract For every large enough $n$, we explicitly construct a body of constant width $2$ that has volume less than $0.9^{n} \textrm{Vol}(\mathbb{B}^{n}$), where ${{\mathbb{B}}}^{n}$ is the unit ball in $\mathbb{R}^{n}$. This answers a question of O. Schramm.
Authors
- Danylo Radchenko (ORCID: https://orcid.org/0000-0003-1457-6214)
- Andriy Prymak (ORCID: https://orcid.org/0000-0002-5022-0154)
- Andriy Bondarenko (ORCID: https://orcid.org/0000-0002-2303-8525)
- Fëdor Nazarov (ORCID: https://orcid.org/0000-0003-2892-3336)
- Arman Arman
Institutions
- Kent State University (US)
- Norwegian University of Science and Technology (NO)
- Université de Lille (FR)
- Laboratoire Paul Painlevé (FR)
- University of Manitoba (CA)
Publication Details
- Journal
- International Mathematics Research Notices
- Published
- 2025-02-01
- DOI
- https://doi.org/10.1093/imrn/rnaf020
- Primary Topic
- Point processes and geometric inequalities
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Science Foundation
- Norges Forskningsråd
- Natural Sciences and Engineering Research Council of Canada
- Division of Mathematical Sciences