Due to the “uncontrollable behavior“ of the inner parallel bodies of a convex body K ⊂ ℝ n regarding its boundary structure, it is not possible to get precise formulae for their volume/quermassintegrals, contrary to the case of the outer parallel bodies. In this paper we provide (sharp) bounds for the quermassintegrals of the inner parallel bodies, studying previously some particular properties of their boundary in terms of their outer normal vectors.
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机译：由于凸体K⊂ n 的内部平行体的边界结构具有“不可控制的行为”，因此与之相反，不可能获得精确的体积/量子积分公式。外部平行体。在本文中，我们为内部平行体的量子共积分提供了（尖锐的）边界，并根据它们的外部法向矢量预先研究了其边界的某些特定属性。
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