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The log-Brunn-Minkowski inequality in mathbb{R}³

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arxiv 1810.05775 v1 pith:2SXGCFQD submitted 2018-10-13 math.DG

The log-Brunn-Minkowski inequality in mathbb{R}³

classification math.DG
keywords inequalitylog-brunn-minkowskibodiesbrunn-minkowskiconvexmathbbclassicalestablishes
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B\"or\"oczky, Lutwak, Yang and Zhang recently proved the log-Brunn-Minkowski inequality which is stronger than the classical Brunn-Minkowski inequality for two origin-symmetric convex bodies in the plane. This paper establishes the log-Brunn-Minkowski, log-Minkowski, $L_p$-Minkowski and $L_p$-Brunn-Minkowski inequalities for two convex bodies in $\mathbb{R}^3$.

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