Langharst, D., & Xi, D. (2024). General higher order 𝐿P mean zonoids. Proceedings of the American Mathematical Society, 152(12), 5299–5311. https://doi.org/10.1090/proc/16914
E104-06 - Forschungsbereich Konvexe und Diskrete Geometrie
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Journal:
Proceedings of the American Mathematical Society
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ISSN:
0002-9939
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Date (published):
2024
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Number of Pages:
13
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Publisher:
AMER MATHEMATICAL SOC
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Peer reviewed:
Yes
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Keywords:
projection bodies; Centroid bodies; Lᴾ Busemann-Petty centroid inequality; radial mean bodies; mean zonoids
en
Abstract:
Abstract. In 1970, Schneider introduced the mth-order difference body and the associated Rogers-Shephard inequality. Recently, Haddad, Langharst, Putterman, Roysdon and Ye expanded the concept to a burgeoning mth-order
Brunn-Minkowski theory. In 1991, Zhang introduced mean zonoids of a convex body, which was extended to the Firey-Brunn-Minkowski theory setting by Xi, Guo and Leng in 2014. In this note, we extend these L^p mean zonoids to the mth-order setting and establish the associated isoperimetric inequality
