A note on an Lp-Brunn-Minkowski inequality for convex measures in the unconditional case

Arnaud Marsiglietti

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Abstract

We consider a different Lp-Minkowski combination of compact sets in Rn than the one introduced by Firey and we prove an L p-Brunn-Minkowski 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 ↦ μ(t1/pA), p ∈ (0,1), for unconditional convex measures μ and unconditional convex body A in Rn. 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.

Original languageEnglish (US)
Pages (from-to)187-200
Number of pages14
JournalPacific Journal of Mathematics
Volume277
Issue number1
DOIs
StatePublished - 2015

Keywords

  • (B)-conjecture
  • Brunn-Minkowski-firey theory
  • Convex body
  • Convex measure
  • L-Minkowski combination

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