Mean dual and harmonic cross-sectional measures

Erwin Lutwak

doi:10.1007/BF02413172

Mean dual and harmonic cross-sectional measures

Erwin Lutwak

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English (US)
Pages (from-to)	139-148
Number of pages	10
Journal	Annali di Matematica Pura ed Applicata, Series 4
Volume	119
Issue number	1
DOIs	https://doi.org/10.1007/BF02413172
State	Published - Dec 1979

ASJC Scopus subject areas

Applied Mathematics

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10.1007/BF02413172

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Mean dual and harmonic cross-sectional measures

Abstract

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