Mixed width-integrals of convex bodies

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)249-253
Number of pages5
JournalIsrael Journal of Mathematics
Volume28
Issue number3
DOIs
StatePublished - Sep 1977

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Convex Body
Mixed Volume
Isoperimetric Inequality
Concurrent
Cross section
Generalise

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Mixed width-integrals of convex bodies. / Lutwak, Erwin.

In: Israel Journal of Mathematics, Vol. 28, No. 3, 09.1977, p. 249-253.

Research output: Contribution to journalArticle

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