Please use this identifier to cite or link to this item:
https://doi.org/10.1007/s00039-023-00647-6
DC Field | Value | |
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dc.title | A nonabelian Brunn–Minkowski inequality | |
dc.contributor.author | Jing, Yifan | |
dc.contributor.author | Tran, Chieu-Minh | |
dc.contributor.author | Zhang, Ruixiang | |
dc.date.accessioned | 2023-07-10T07:32:17Z | |
dc.date.available | 2023-07-10T07:32:17Z | |
dc.date.issued | 2023-07-05 | |
dc.identifier.citation | Jing, Yifan, Tran, Chieu-Minh, Zhang, Ruixiang (2023-07-05). A nonabelian Brunn–Minkowski inequality. Geometric and Functional Analysis. ScholarBank@NUS Repository. https://doi.org/10.1007/s00039-023-00647-6 | |
dc.identifier.issn | 1016-443X | |
dc.identifier.issn | 1420-8970 | |
dc.identifier.uri | https://scholarbank.nus.edu.sg/handle/10635/242987 | |
dc.description.abstract | <jats:title>Abstract</jats:title><jats:p>Henstock and Macbeath asked in 1953 whether the Brunn–Minkowski inequality can be generalized to nonabelian locally compact groups; questions along the same line were also asked by Hrushovski, McCrudden, and Tao. We obtain here such an inequality and prove that it is sharp for helix-free locally compact groups, which includes real linear algebraic groups, Nash groups, semisimple Lie groups with finite center, solvable Lie groups, etc. The proof follows an induction on dimension strategy; new ingredients include an understanding of the role played by maximal compact subgroups of Lie groups, a necessary modified form of the inequality which is also applicable to nonunimodular locally compact groups, and a proportionated averaging trick. </jats:p> | |
dc.publisher | Springer Science and Business Media LLC | |
dc.source | Elements | |
dc.type | Article | |
dc.date.updated | 2023-07-07T15:51:34Z | |
dc.contributor.department | MATHEMATICS | |
dc.description.doi | 10.1007/s00039-023-00647-6 | |
dc.description.sourcetitle | Geometric and Functional Analysis | |
dc.published.state | Unpublished | |
Appears in Collections: | Staff Publications Elements |
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