{"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/symplectic-embeddings-of-4-dimensional-1","title":"Symplectic embeddings of 4-dimensional ellipsoids","arxiv_id":"0801.4665","date":"2008-01-30","proceeding":null,"authors":["Dusa McDuff"],"abstract":"We show how to reduce the problem of symplectically embedding one 4-dimensional rational ellipsoid into another to a problem of embedding disjoint unions of balls into appropriate blow ups of \\C P^2. For example, the problem of embedding the ellipsoid E(1,k) into a ball B is equivalent to that of embedding k disjoint equal balls into \\C P^2, and so can be solved by the work of Gromov, McDuff--Polterovich and Biran. (Here k is the ratio of the area of the major axis to that of the minor axis.) As a consequence we show that the ball may be fully filled by the ellipsoid E(1,k) for k=1,4 and all k\\ge 9, thus answering a question raised by Hofer.","url_abs":"https://arxiv.org/abs/0801.4665v3","url_pdf":"https://arxiv.org/pdf/0801.4665v3.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":"symplectic-embeddings-of-4-dimensional-1","repo_url":"https://github.com/mjusher/symplectic-embeddings","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","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}