The Brunn-Minkowski-Firey inequality for nonconvex sets

Erwin Lutwak, Deane Yang, Gaoyong Zhang

Research output: Contribution to journalArticlepeer-review


The definition of Minkowski-Firey Lp-combinations is extended from convex bodies to arbitrary subsets of Euclidean space. The Brunn-Minkowski-Firey inequality (along with its equality conditions), previously established only for convex bodies, is shown to hold for compact sets.

Original languageEnglish (US)
Pages (from-to)407-413
Number of pages7
JournalAdvances in Applied Mathematics
Issue number2
StatePublished - Feb 2012


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

ASJC Scopus subject areas

  • Applied Mathematics


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