Abstract In 2006, Schuster introduced the radial Blaschke-Minkowski homomorphisms. In this article, associating with the star duality of star bodies and dual quermassintegrals, we establish Brunn-Minkowski inequalities and monotonic inequality for the radial Blaschke-Minkowski homomorphisms. In addition, we consider its Shephard-type problems and give a positive form and a negative answer, respectively.

中文翻译：

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径向 Blaschke-Minkowski 同态的星二元性的一些不等式

摘要 2006 年，Schuster 引入了径向 Blaschke-Minkowski 同态。在本文中，结合星体的星对偶性和对偶quermassintegrals，我们建立了径向Blaschke-Minkowski同态的Brunn-Minkowski不等式和单调不等式。此外，我们考虑其 Shephard 型问题并分别给出肯定形式和否定答案。