Mean dual and harmonic cross-sectional measures

Erwin Lutwak

Research output: Contribution to journalArticlepeer-review


The mean dual cross-sectional measures are introduced. They are shown to satisfy a cyclic inequality similar to that satisfied by the cross-sectional measures (Quermassintegrale). A new representation of the dual cross-sectional measures is used to obtain inequalities relating the mean dual cross-sectional measures and the harmonic cross-sectional measures (Harmonische Quermassintegrale) of Hadwiger. An inequality between the volume and the harmonic cross-sectional measures of a convex body is presented. An inequality stronger than the Urysohn inequality (the harmonic Urysohn inequality) is proven. Strengthened versions of other inequalities previously obtained by the author are also presented.

Original languageEnglish (US)
Pages (from-to)139-148
Number of pages10
JournalAnnali di Matematica Pura ed Applicata, Series 4
Issue number1
StatePublished - Dec 1979

ASJC Scopus subject areas

  • Applied Mathematics


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