Open AccessA mixed volume from the anisotropic Riesz‐potential
Author(s) -
Hou Shaoxiong,
Xiao Jie,
Ye Deping
Publication year - 2018
Publication title -
transactions of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.43
H-Index - 7
ISSN - 2052-4986
DOI - 10.1112/tlm3.12012
Subject(s) - minkowski space , anisotropy , lorentz transformation , mathematics , riesz potential , type (biology) , volume (thermodynamics) , inequality , space (punctuation) , mathematical analysis , lorentz space , pure mathematics , physics , mathematical physics , classical mechanics , quantum mechanics , computer science , ecology , biology , operating system
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.