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)|
|Number of pages||10|
|Journal||Annali di Matematica Pura ed Applicata, Series 4|
|State||Published - Dec 1979|
ASJC Scopus subject areas
- Applied Mathematics