Lombardi, N., & Saorín Gómez, E. (2023). Mean radii of symmetrizations of a convex body. Beitraege Zur Algebra Und Geometrie. https://doi.org/10.1007/s13366-023-00698-8
E104-06 - Forschungsbereich Konvexe und Diskrete Geometrie E104 - Institut für Diskrete Mathematik und Geometrie
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Journal:
Beitraege zur Algebra und Geometrie
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ISSN:
0138-4821
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Date (published):
6-Jun-2023
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Number of Pages:
26
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Publisher:
Springer
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Peer reviewed:
Yes
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Keywords:
mean radii; quermassintegral; inequality
en
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.
