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Brunn-Minkowski Inequality for [Formula: see text]-Convolution Bodies via Ball's Bodies

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We consider the problem of finding the best function φn:[0,1]→R such that for any pair of convex bodies K,L∈Rn the following Brunn-Minkowski type inequality holds |K+θL|1n≥φn(θ)(|K|1n+|L|1n),where K+θL is the θ-c... ...