A NOTE ON AN LP-BRUNN-MINKOWSKI INEQUALITY FOR CONVEX MEASURES IN THE UNCONDITIONAL CASE By
نویسنده
چکیده
We consider a different L-Minkowski combination of compact sets in R than the one introduced by Firey and we prove an L-BrunnMinkowski inequality, p ∈ [0, 1], for a general class of measures called convex measures that includes log-concave measures, under unconditional assumptions. As a consequence, we derive concavity properties of the function t 7→ μ(t 1 pA), p ∈ (0, 1], for unconditional convex measures μ and unconditional convex body A in R. We also prove that the (B)-conjecture for all uniform measures is equivalent to the (B)conjecture for all log-concave measures, completing recent works by Saroglou.
منابع مشابه
A note on an L-Brunn-Minkowski inequality for convex measures in the unconditional case
We consider a different L-Minkowski combination of compact sets in R than the one introduced by Firey and we prove an L-BrunnMinkowski inequality, p ∈ [0, 1], for a general class of measures called convex measures that includes log-concave measures, under unconditional assumptions. As a consequence, we derive concavity properties of the function t 7→ μ(t 1 pA), p ∈ (0, 1], for unconditional con...
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