{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/small-volume-bodies-of-constant-width","title":"Small volume bodies of constant width","arxiv_id":"2405.18501","date":"2024-05-28","proceeding":null,"authors":["Andrii Arman","Andriy Bondarenko","Fedor Nazarov","Andriy Prymak","Danylo Radchenko"],"abstract":"For every large enough $n$, we explicitly construct a body of constant width $2$ that has volume less than $0.9^n \\text{Vol}(\\mathbb{B}^{n}$), where $\\mathbb{B}^{n}$ is the unit ball in $\\mathbb{R}^{n}$. This answers a question of O.~Schramm.","url_abs":"https://arxiv.org/abs/2405.18501v2","url_pdf":"https://arxiv.org/pdf/2405.18501v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"small-volume-bodies-of-constant-width","repo_url":"https://github.com/microsoft/renderformer","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}