Israel Journal of Mathematics

, Volume 28, Issue 3, pp 249–253 | Cite as

Mixed width-integrals of convex bodies

  • Erwin Lutwak
Article
Received:

Abstract

The mixed width-integrals are defined and shown to have properties similar to those of the mixed volumes of Minkowski. An inequality is established for the mixed width-integrals analogous to the Fenchel-Aleksandrov inequality for the mixed volumes. An isoperimetric inequality (involving the mixed width-integrals) is presented which generalizes an inequality recently obtained by Chakerian and Heil. Strengthened versions of this general inequality are obtained by introducing indexed mixed width-integrals. This leads to an isoperimetric inequality similar to Busemann’s inequality involving concurrent cross-sections of convex bodies.

Keywords

Convex Body Isoperimetric Inequality Constant Width Mixed Volume General Inequality 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Hebrew University 1977

Authors and Affiliations

  • Erwin Lutwak
    • 1
  1. 1.Polytechnic Institute of New YorkBrooklynUSA

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