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We study the relation between some successive and mean radii of a convex body and its Steiner, Schwarz, and Minkowski symmetral. In particular, we are interested in the mean radii. Based on the convexity of some of the radii of a (particular) parallel chord movement of convex bodies, we prove that the Steiner symmetral does not increase the mean outer radii. Results of the same type hold for the Schwarz and Minkowski symmetrals.
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry – Springer Journals
Published: Jun 6, 2023
Keywords: Mean radii; Symmetrization; Inequality; Primary 52A20; Secondary 52A40
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