A mixed volume from the anisotropic Riesz‐potential. (5th January 2018)

• Record Type: Journal Article
• Authors: Hou, Shaoxiong; Xiao, Jie; Ye, Deping
• Is Part Of: Transactions of the London Mathematical Society. Volume 5:Number 1(2018)
• Page Start: 71
• Page End: 96
• Publication Date: 2018-01-05
• Subjects: 52A38 -- 53A15 -- 53A30 (primary); Mathematics -- Periodicals; 510.5
• DOI: 10.1112/tlm3.12012
• Languages: English
• ISSNs: 2052-4986

Abstract

Abstract: As a geometrical understanding of the maximal gravitational potential in computational and mathematical physics, this paper investigates a mixed volume induced by the so‐called anisotropic Riesz‐potential and establishes a reverse Minkowski‐type inequality. It turns out that such a mixed volume is equal to the anisotropic Riesz‐capacity and has connections with the anisotropic sup‐Riesz‐potential space. Two restrictions on the Lorentz spaces in terms of the anisotropic Riesz‐capacity are also characterized. Besides, we also prove a Minkowski‐type inequality and a log‐Minkowski‐type inequality as well as its reverse form.