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 2012

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Brunn-Minkowski Inequality
Convex Body
Mixed Volume
Unit ball
Banach space
Family

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

The log-Brunn-Minkowski inequality. / Böröczky, Károly J.; Lutwak, Erwin; Yang, Deane; Zhang, Gaoyong.

In: Advances in Mathematics, Vol. 231, No. 3-4, 10.2012, p. 1974-1997.

Research output: Contribution to journalArticle

Böröczky, Károly J. ; Lutwak, Erwin ; Yang, Deane ; Zhang, Gaoyong. / The log-Brunn-Minkowski inequality. In: Advances in Mathematics. 2012 ; Vol. 231, No. 3-4. pp. 1974-1997.
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