Divergence for s-concave and log concave functions

Umut Caglar, Elisabeth M. Werner

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


We prove new entropy inequalities for log concave and s-concave functions that strengthen and generalize recently established reverse log Sobolev and Poincaré inequalities for such functions. This leads naturally to the concept of f-divergence and, in particular, relative entropy for s-concave and log concave functions. We establish their basic properties, among them the affine invariant valuation property. Applications are given in the theory of convex bodies.

Original languageEnglish (US)
Pages (from-to)219-247
Number of pages29
JournalAdvances in Mathematics
StatePublished - Jun 1 2014

Bibliographical note

Copyright 2014 Elsevier B.V., All rights reserved.


  • Affine isoperimetric inequalities
  • Divergence
  • Entropy
  • Log Sobolev inequalities


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