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Mixed width-integrals of convex bodies

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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.

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Authors and Affiliations

  1. Polytechnic Institute of New York, 11201, Brooklyn, New York, USA

    Erwin Lutwak

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  1. Erwin Lutwak
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Lutwak, E. Mixed width-integrals of convex bodies. Israel J. Math. 28, 249–253 (1977). https://doi.org/10.1007/BF02759811

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  • DOI: https://doi.org/10.1007/BF02759811

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