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Title: A nonabelian Brunn–Minkowski inequality
Authors: Jing, Yifan
Tran, Chieu-Minh 
Zhang, Ruixiang
Issue Date: 5-Jul-2023
Publisher: Springer Science and Business Media LLC
Citation: Jing, Yifan, Tran, Chieu-Minh, Zhang, Ruixiang (2023-07-05). A nonabelian Brunn–Minkowski inequality. Geometric and Functional Analysis. ScholarBank@NUS Repository.
Abstract: AbstractHenstock 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.
Source Title: Geometric and Functional Analysis
ISSN: 1016-443X
DOI: 10.1007/s00039-023-00647-6
Appears in Collections:Staff Publications

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