A general framework of polar Brunn-Minkowski theory that unifies the Orlicz Brunn-Minkowski inequality, the Lp Brunn-Minkowski inequality for p ∈(0,1) and the logBrunn-Minkowski inequality all for polar bodies is provided. It is shown that this general polar φ Brunn-Minkowski inequality is equivalent to a general polar φ Minkowski mixed volume inequality.
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