The Brunn-Minkowski Inequality and Nonconvex Sets

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Abstract

We improve the Brunn-Minkowski inequality for nonconvex sets. Besides the volume of the sets, our estimate depends on the volume of the convex hull of one of the sets. The estimate is asymptotically the best possible if this set is fixed and the size of the other tends to infinity.

Original languageEnglish
Pages (from-to)337-348
Number of pages12
JournalGeometriae Dedicata
Volume67
Issue number3
DOIs
Publication statusPublished - Jan 1 1997

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Keywords

  • Convex hull
  • Convexity
  • Sumsets
  • Volume

ASJC Scopus subject areas

  • Geometry and Topology

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