Lp$L_p$‐cosine transform of the (p,q)${(p,q)}$‐th dual curvature measure

Niufa Fang, Hejun Wang and Zengle Zhang

Mathematische Nachrichten, 2022, vol. 295, issue 12, 2393-2404

Abstract: The (p,q)$(p,q)$‐th dual curvature measure was introduced by Lutwak, Yang and Zhang. In this paper, we study the Lp$L_p$ cosine transform of the (p,q)$(p,q)$‐th dual curvature measure which defines a new convex body. We prove that the new convex body unifies the Lp$L_p$ Petty projection body and the Lp$L_p$ centroid body. The corresponding affine isoperimetric inequality is also obtained. It is an extension of the known Lp$L_p$ Petty projection inequality.

Date: 2022
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https://doi.org/10.1002/mana.202000084

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