Geometriae Dedicata

, Volume 67, Issue 3, pp 337–348

The Brunn–Minkowski Inequality and Nonconvex Sets

  • IMRE Z. Ruzsa

DOI: 10.1023/A:1004958110076

Cite this article as:
Ruzsa, I.Z. Geometriae Dedicata (1997) 67: 337. doi:10.1023/A:1004958110076


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.

volume convexity convex hull sumsets. 

Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • IMRE Z. Ruzsa
    • 1
  1. 1.Mathematical Institute of the Hungarian Academy of Sciences, Pf. 127BudapestHungary

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