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Research Article | Open Access

Dual Brunn-Minkowski inequality for C-star bodies

Xudong Wang( ), Tingting Xiang
School of Mathematics and Statistics, Shaanxi Normal University, Xi'an 710119, Shaanxi, China
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Abstract

In this paper, we introduced the concept of C-star bodies in a fixed pointed closed convex cone C and studied the dual mixed volume for C-star bodies. For C-star bodies, we established the corresponding dual Brunn-Minkowski inequality, dual Minkowski inequality, and dual Aleksandrov-Fenchel inequality. Moveover, we found that the dual Brunn-Minkowski inequality for C-star bodies can strengthen the Brunn-Minkowski inequality for C-coconvex sets.

Keywords

C-star bodiesLutwak sumdual mixed volumedual Brunn-Minkowski inequality
CLC number: 52A30, 52A39, 52A40

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AIMS Mathematics
Volume 9 Issue 4,
April 2024
Pages 7834-7847
DOI: 10.3934/math.2024381

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Cite this article:
Wang X, Xiang T. Dual Brunn-Minkowski inequality for C-star bodies. AIMS Mathematics, 2024, 9(4): 7834-7847. https://doi.org/10.3934/math.2024381

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Received: 18 January 2024
Revised: 05 February 2024
Accepted: 18 February 2024
Published: 15 April 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)