A Mixed Volumetry for the Anisotropic Logarithmic Potential

Hou, Shaoxiong; Xiao, Jie

doi:10.1007/s12220-017-9895-z

Cited by 7 publications

(3 citation statements)

References 6 publications

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“…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.…”

Section: Introductionmentioning

confidence: 94%

The affine log-Aleksandrov–Fenchel inequality

Zhao¹

2023

Revista De La Unión Matemática Argentina

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We establish a new affine log-Aleksandrov-Fenchel inequality for mixed affine quermassintegrals by introducing new concepts of affine and multiple affine measures, and using the newly established Aleksandrov-Fenchel inequality for multiple mixed affine quermassintegrals. Our new inequality yields as special cases the classical Aleksandrov-Fenchel inequality and the Lp-affine log-Aleksandrov-Fenchel inequality. The affine log-Minkowski and log-Aleksandrov-Fenchel inequalities are also derived.

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Section: Introductionmentioning

confidence: 94%

The affine log-Aleksandrov–Fenchel inequality

Zhao¹

2023

Revista De La Unión Matemática Argentina

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“…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.…”

Section: Introductionmentioning

confidence: 99%

The affine Orlicz log-Minkowki inequality

ZHAO¹

2022

CJM

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In this paper, we establish an affine Orlicz log-Minkowki inequality for the affine quermassintegrals by introducing new concepts of affine measures and Orlicz mixed affine measures, and using the newly established Orlicz affine Minkowski inequality for the affine quermassintegrals. The affine Orlicz log-Minkowski inequality in special case yields $L_{p}$-affine log-Minkowski inequality. The affine log-Minkowski inequality is also derived.

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“…Recently, this logarithmic Minkowski inequality and the conjectured logarithmic Minkowski inequality have attracted extensive attention and research. The recent research on the logarithmic Minkowski and its dual type inequalities can be found in the references [3][4][5][6][7][8][9][10][11][12][13][14][15][16].…”

Section: Introducationmentioning

confidence: 99%

The Dual Orlicz–Aleksandrov–Fenchel Inequality

Zhao

2020

Mathematics

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In this paper, the classical dual mixed volume of star bodies V˜(K1,⋯,Kn) and dual Aleksandrov–Fenchel inequality are extended to the Orlicz space. Under the framework of dual Orlicz-Brunn-Minkowski theory, we put forward a new affine geometric quantity by calculating first order Orlicz variation of the dual mixed volume, and call it Orlicz multiple dual mixed volume. We generalize the fundamental notions and conclusions of the dual mixed volume and dual Aleksandrov-Fenchel inequality to an Orlicz setting. The classical dual Aleksandrov-Fenchel inequality and dual Orlicz-Minkowski inequality are all special cases of the new dual Orlicz-Aleksandrov-Fenchel inequality. The related concepts of Lp-dual multiple mixed volumes and Lp-dual Aleksandrov-Fenchel inequality are first derived here. As an application, the dual Orlicz–Brunn–Minkowski inequality for the Orlicz harmonic addition is also established.

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A Mixed Volumetry for the Anisotropic Logarithmic Potential

Cited by 7 publications

References 6 publications

The affine log-Aleksandrov–Fenchel inequality

The affine log-Aleksandrov–Fenchel inequality

The affine Orlicz log-Minkowki inequality

The Dual Orlicz–Aleksandrov–Fenchel Inequality

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