Log-Minkowski inequalities for the L p $L_{p}$ -mixed quermassintegrals

Abstract

Böröczky et al. proposed the log-Minkowski problem and established the plane log-Minkowski inequality for origin-symmetric convex bodies. Recently, Stancu proved the log-Minkowski inequality for mixed volumes; Wang, Xu, and Zhou gave the L p version of Stancu's results. In this paper, we define the L p-mixed quermassintegrals probability measure and obtain the log-Minkowski inequality for the L p-mixed quermassintegrals. As its application, we establish the L p-mixed affine isoperimetric inequality. In addition, we also consider the dual log-Minkowski inequalities for the L p-dual mixed quermassintegrals.

The affine log-Aleksandrov–Fenchel inequality

“…Recently, the log-Minkowski inequality and the log-Aleksandrov-Fenchel inequality and its dual form have attracted extensive attention and research: see references [1,3,4,6,7,8,12,13,14,18,17,19,20,21,22,23]. In this paper, we generalize the log-Minkowski inequality (1.1) and the log-Aleksandrov-Fenchel inequality (1.2) to the mixed affine quermassintegrals.…”

Rational design of MoS2-supported Cu single-atom catalysts by machine learning potential for enhanced peroxidase-like activity

“…23 Co-MoS 2 , 24 single Ru atom-doped MoS 2 supported by carbon cloth (Ru-MoS 2 /CC) 25 and Al single atom-doped MoS 2 have also been studied for enhancing the enzymatic activity of MoS 2 . 26 As a cheap and readily available material, non-noble Cu is also expected to be applied in 2D MoS 2 supported SACs. A 2D MoS 2 -supported Cu single atom catalyst, denoted as Cu@MoS 2 , has been successfully synthesized and applied as a high-performance electrocatalyst for overall water splitting by altering the surface charge distribution and electronic band structure, 27 in efficient hydrogen evolution due to changes in atomic coordination structures, 28 and in low-temperature CO oxidation due to the charge transfer between the SAC and the substrate.…”

The affine Orlicz log-Minkowki inequality

“…Recently, the logarithmic Minkowski inequality and its dual form have attracted extensive attention and research, and the recent research can be found in the references [1], [3], [4], [6], [7], [8], [12], [13], [14], [17], [18], [19], [20], [21], [22] and [23]. In the paper, we generalize the usual volumes and log-Minkowski inequality (1.1) to the affine quermassintegrals and Orlicz space, respectively.…”