Summary
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.
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Entrata in Redazione il 13 luglio 1977.
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Lutwak, E. Mean dual and harmonic cross-sectional measures. Annali di Matematica 119, 139–148 (1979). https://doi.org/10.1007/BF02413172
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DOI: https://doi.org/10.1007/BF02413172