$L_{p}$-dual Brunn–Minkowski inequality for intersection bodies

Weidong Wang

doi:10.4171/pm/2142

JournalspmVol. 82, No. 3/4pp. 387–401

$L_{p}$ -dual Brunn–Minkowski inequality for intersection bodies

Weidong Wang
China Three Gorges University, Yichang, P. R. China
ORCID

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Abstract

In 2003, associated with the radial Minkowski additions of star bodies, Zhao and Leng established the dual Brunn–Minkowski inequality for intersection bodies. In this paper, associated with the $L_{p}$ -radial Minkowski combinations of star bodies, we firstly prove the $L_{p}$ -dual Brunn–Minkowski inequality for intersection bodies. Further, associated with the $L_{p}$ -Minkowski combinations of convex bodies, we give the $L_{p}$ -Brunn–Minkowski inequality for star dualities of intersection bodies.

Cite this article

Weidong Wang, $L_{p}$ -dual Brunn–Minkowski inequality for intersection bodies. Port. Math. 82 (2025), no. 3/4, pp. 387–401

DOI 10.4171/PM/2142