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In this article, some kinematic formulas for dual quermassintegral of star bodies and for chord power integrals of convex bodies are established by using dual mixed volumes. These formulas are the extensions of the fundamental kinematic formula involving quermassintegral to the case of dual quermassintegral and chord power integrals. 相似文献
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In this paper, we obtain a formula relating the chord power integrals of a convex body K and the dual quermassintegrals of its radial pth mean body RpK. With this, a relation among the chord power integrals of a convex body K under dilation transformations is found. As an interesting application, some geometric inequalities between the dual quermassintegrals of RpK and the volume of K, which are equivalent to the isoperimetric-type inequalities of chord power integrals, are also established. 相似文献
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本文利用对偶混合体积建立平移积分几何中的对偶运动公式.这些公式是将关于均质积分的基本运动公式推广到对偶均质积分和对偶混合体积情形. 相似文献
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Translative versions of the principal kinematic formula for quermassintegrals of convex bodies are studied. The translation integral is shown to be a sum of Crofton type integrals of mixed volumes. As corollaries new integral formulas for mixed volumes are obtained. For smooth centrally symmetric bodies the functionals occurring in the principal translative formula are expressed by measures on Grassmannians which are related to the generating measures of the bodies.Dedicated to Professor Otto Haupt with best wishes on his 100th birthday 相似文献
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我们引入星体的径向弦长积分的概念,并研究了它的性质.作为它的应用,建立了径向弦长积分的循环不等式、Brunn-Minkowski型不等式和对偶Bieberbach型不等式. 相似文献
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L_p-混合质心体和对偶L_p-混合质心体 总被引:1,自引:0,他引:1
本文引进了L_p-混合质心体Γ_(p,i)K、对偶L_p-混合质心体Γ_(-p,i)K和R~n中星体K和L的L_p-混合调和Blaschke加K+_pL的概念,成功地解决了L_p-混合质心体和对偶L_p-混合质心体的Shephard型问题.并且结合星体的L_p-混合调和Blaschke加的概念,分别建立了L_p-混合质心体的均质积分和对偶均质积分的Brunn-Minkowski型不等式.所获结论推广了已有文献的结果. 相似文献
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