Dual Brunn-Minkowski inequality for $ C $-star bodies

Xudong Wang; Tingting Xiang; Xudong Wang; Tingting Xiang

doi:10.3934/math.2024381

AIMS Mathematics

2024, Volume 9, Issue 4: 7834-7847. doi: 10.3934/math.2024381

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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

Received: 18 January 2024 Revised: 05 February 2024 Accepted: 18 February 2024 Published: 23 February 2024
MSC : 52A30, 52A39, 52A40

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.
- $ C $-star bodies,
- Lutwak sum,
- dual mixed volume,
- dual Brunn-Minkowski inequality
Citation: Xudong Wang, Tingting Xiang. Dual Brunn-Minkowski inequality for $ C $-star bodies[J]. AIMS Mathematics, 2024, 9(4): 7834-7847. doi: 10.3934/math.2024381

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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.

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