2019/04/05 by Michael Roysdon, Roysdon, Michael
Biochemistry, Genetics and Molecular Biology · Mathematics · #28A25 #FOS: Mathematics #Mathematical Inequalities and Applications #Metric Geometry (math.MG) #Point processes and geometric inequalities #Primary 52A40 #Prion Diseases and Protein Misfolding #Secondary 52A20
paper · pdf · doi:10.48550/arxiv.1904.03255
openalex publication_date 2019/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we address the following question: given a measure μ on ℝn, does there exists a constant C>0 such that, for any m-dimensional subspace H ⊂ ℝn and any convex body K ⊂ ℝn, the following sectional Rogers-Shephard type inequality holds: μ((K-K) ∩ H) ≤ C supy ∈ ℝn μ(K ∩ (H+y))? We show that this inequality is affirmative in the class of measures with radially decreasing densities with the constant C(n,m) = \binomn+mm. We also prove marginal inequalities of the Rogers-Shephard type for ((1)/(s))-concave, 0 ≤ s < ∞, and logarithmically concave functions.