On the analogue of the concavity of entropy power in the Brunn-Minkowski theory

Matthieu Fradelizi, Arnaud Marsiglietti

Research output: Contribution to journalArticle

6 Scopus citations

Abstract

Elaborating on the similarity between the entropy power inequality and the Brunn-Minkowski inequality, Costa and Cover conjectured the 1n-concavity of the outer parallel volume of measurable sets as an analogue of the concavity of entropy power. We investigate this conjecture and study its relationship with geometric inequalities.

Original languageEnglish (US)
Pages (from-to)1-20
Number of pages20
JournalAdvances in Applied Mathematics
Volume57
DOIs
StatePublished - Jun 2014

Keywords

  • Brunn-Minkowski
  • Entropy power
  • Isoperimetric inequality
  • Parallel set
  • Parallel volume

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