The log-Minkowski measure of asymmetry for convex bodies

Jin, Hailin

doi:10.1007/s10711-017-0302-5

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Introduction2

Theorem 1b (The Log-minkowski Inequality For Mixed Quermass1

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2019

2023

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Cited by 6 publications

(3 citation statements)

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“…The log-Minkowski inequality belongs to log-Minkowski theory. For more research on log-Minkowski theory, we may refer to [13][14][15][16][17][18][19][20][21][22].…”

Section: Theorem 1b (The Log-minkowski Inequality For Mixed Quermassmentioning

confidence: 99%

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

Wang

2019

J Inequal Appl

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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.

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“…The log-Minkowski inequality belongs to log-Minkowski theory. For more research on log-Minkowski theory, we may refer to [13][14][15][16][17][18][19][20][21][22].…”

Section: Theorem 1b (The Log-minkowski Inequality For Mixed Quermassmentioning

confidence: 99%

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

Wang

2019

J Inequal Appl

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“…For the new development of the research of the Minkowski measure of asymmetry, see Refs. [2][3][4][5][6][7].…”

Section: Introductionmentioning

confidence: 99%

“…A special measure of asymmetry for convex bodies of constant width in R 2 was introduced by Groemer and Wallen [9] . The Minkowski measure of asymmetry for convex bodies of constant width was studied by Guo and Jin [3,5,6,10,11] . In the sense of Minkowski measure of asymmetry, the complete bodies of the regular simplex are the most asymmetric convex bodies of constant width, and the Euclidean balls are the most symmetric convex bodies of constant width.…”

Section: Introductionmentioning

confidence: 99%