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Mean radii of symmetrizations of a convex body

Mean radii of symmetrizations of a convex body 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry Springer Journals

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References (30)

Publisher
Springer Journals
Copyright
Copyright © The Managing Editors 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
ISSN
0138-4821
eISSN
2191-0383
DOI
10.1007/s13366-023-00698-8
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Beiträge zur Algebra und Geometrie / Contributions to Algebra and GeometrySpringer Journals

Published: Jun 6, 2023

Keywords: Mean radii; Symmetrization; Inequality; Primary 52A20; Secondary 52A40

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