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arXiv · 1910.05367

Isoperimetric relations for inner parallel bodies

María A. Hernández Cifre·Eugenia Saorín Gómez
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Abstract

We analyze aspects of the behavior of the family of inner parallel bodies of a convex body for the isoperimetric quotient and deficit of arbitrary quermassintegrals. By means of technical boundary properties of the so-called form body of a convex body and similar constructions for inner parallel bodies, we point out an erroneous use of a relation between the latter bodies in two different works. We correct these results, limiting them to convex bodies having a very precise boundary structure.

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María A. Hernández Cifre, Eugenia Saorín Gómez. 2019-10-11. Isoperimetric relations for inner parallel bodies. https://arxiv.org/abs/1910.05367

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