A local proof of the dimensional Prékopa's theorem

2014/04/17 by Van Hoang Nguyen, Nguyen, Van Hoang · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · #26A51 #Bounded function #Combinatorics #Derivative (finance) #Diffusion and Search Dynamics #Discrete mathematics #FOS: Mathematics #Function (biology) #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Mathematical analysis #Mathematics #Point processes and geometric inequalities #Pure mathematics #math.FA #msc:26A51

paper · pdf · doi:10.48550/arxiv.1404.4525

9 pages, to appear in J. Math. Anal. Appl

arxiv created 2014/04/17 · openalex publication_date 2014/04/17 · arxiv updated 2014/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The aim of this paper is to find an expression for second derivative of the function ϕ(t) defined by ϕ(t) = \lt(∫_V \vphi(t,x)^-β dx\rt)^-\frac1\be -n, β\not= n, where U⊂ \R and V⊂ \Rⁿ are open bounded subsets, and \vphi: U× V→ \R₊ is a C²-smooth function. As a consequence, this result gives us a direct proof of the dimensional Prékopa's theorem based on a local approach.

Citations

• The Brunn-Minkowski inequality

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