On inner parallel bodies and quermassintegrals
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- Hernández Cifre, M.A. & Saorín, E. Isr. J. Math. (2010) 177: 29. doi:10.1007/s11856-010-0037-6
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Due to the “uncontrollable behavior“ of the inner parallel bodies of a convex body K ⊂ ℝn 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.