Abstract
For strictly increasing concave functions \({\varphi}\) whose inverse functions are log-concave, the \({\varphi}\)-Brunn–Minkowski inequality for planar convex bodies is established. It is shown that for convex bodies in \({\mathbb{R}^n}\) the \({\varphi}\)-Brunn–Minkowski is equivalent to the \({\varphi}\)-Minkowski mixed volume inequalities.
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Research was supported partly by NSFC under Grant 10801140, CSTC under Grant 2013-JCYJ-A00005, CQNU Foundation under Grant 13XLZ05.
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Lv, SJ. The \({\varphi}\)-Brunn–Minkowski inequality. Acta Math. Hungar. 156, 226–239 (2018). https://doi.org/10.1007/s10474-018-0825-8
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DOI: https://doi.org/10.1007/s10474-018-0825-8