The Journal of Geometric Analysis

, Volume 29, Issue 1, pp 299–315 | Cite as

A Reverse Rogers–Shephard Inequality for Log-Concave Functions

  • David Alonso-GutiérrezEmail author


We will prove a reverse Rogers–Shephard inequality for log-concave functions. In some particular cases, the method used for general log-concave functions can be slightly improved, allowing us to prove volume estimates for polars of \(\ell _p\)-diferences of convex bodies under the condition that their polar bodies have opposite barycenters.


Rogers–Shephard inequality Log-concave functions Log-concave measures Geometric inequalities Functional inequalities 

Mathematics Subject Classification

52A20 39B62 



Partially suppored by MINECO Project MTM2016-77710-P.


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Copyright information

© Mathematica Josephina, Inc. 2018

Authors and Affiliations

  1. 1.Área de Análisis Matemático, Departamento de Matemáticas, Facultad de Ciencias, IUMAUniversidad de ZaragozaZaragozaSpain

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