A mixed volume from the anisotropic Riesz‐potential

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.