The log-Brunn-Minkowski inequality

Károly J. Böröczky, Erwin Lutwak, Deane Yang, Gaoyong Zhang

Research output: Contribution to journalArticle

Abstract

For origin-symmetric convex bodies (i.e., the unit balls of finite dimensional Banach spaces) it is conjectured that there exist a family of inequalities each of which is stronger than the classical Brunn-Minkowski inequality and a family of inequalities each of which is stronger than the classical Minkowski mixed-volume inequality. It is shown that these two families of inequalities are "equivalent" in that once either of these inequalities is established, the other must follow as a consequence. All of the conjectured inequalities are established for plane convex bodies.

Original languageEnglish (US)
Pages (from-to)1974-1997
Number of pages24
JournalAdvances in Mathematics
Volume231
Issue number3-4
DOIs
StatePublished - Oct 1 2012

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Keywords

  • Brunn-Minkowski inequality
  • Brunn-Minkowski-Firey inequality
  • Minkowski mixed-volume inequality
  • Minkowski-Firey L -combinations

ASJC Scopus subject areas

  • Mathematics(all)

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