On the Orlicz Minkowski Problem for Polytopes

Huang, Qiuying; He, Bin

doi:10.1007/s00454-012-9434-4

Cited by 107 publications

(75 citation statements)

References 51 publications

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“…The Orlicz centroid inequality for star bodies was introduced in [20]. The other articles advancing the theory can be found in literatures [7,[21][22][23][24][25].…”

Section: Journal Of Function Spacesmentioning

confidence: 99%

Orlicz Mean Dual Affine Quermassintegrals

Zhao

Cheung

2018

Journal of Function Spaces

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Our main aim is to generalize the mean dual affine quermassintegrals to the Orlicz space. Under the framework of dual OrliczBrunn-Minkowski theory, we introduce a new affine geometric quantity by calculating the first Orlicz variation of the mean dual affine quermassintegrals and call it the Orlicz mean dual affine quermassintegral. The fundamental notions and conclusions of the mean dual affine quermassintegrals and the Minkowski and Brunn-Minkowski inequalities for them are extended to an Orlicz setting. The related concepts and inequalities of dual Orlicz mixed volumes are also included in our conclusions. The new Orlicz isoperimetric inequalities in special case yield the -dual Minkowski inequality and Brunn-Minkowski inequality for the mean dual affine quermassintegrals, which also imply the dual Orlicz-Minkowski inequality and dual Orlicz-Brunn-Minkowski inequality.

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“…The Orlicz centroid inequality for star bodies was introduced in [20]. The other articles advancing the theory can be found in literatures [7,[21][22][23][24][25].…”

Section: Journal Of Function Spacesmentioning

confidence: 99%

Orlicz Mean Dual Affine Quermassintegrals

Zhao

Cheung

2018

Journal of Function Spaces

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“…Then, still in the case with ϕ(t) → +∞ as t → 0, Huang and He proved in [21] that one can get rid of the assumption that μ is an even measure. For the moment and in order to fix ideas, one may take ϕ(x, s) = g(x)s p−1 + λs β−1 for p, β > 2:…”

Section: Introductionmentioning

confidence: 97%

The planar Orlicz Minkowski problem in the L1-sense

Sun

2015

Advances in Mathematics

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“…Then Lutwak [22] introduced the concept of L p -mixed volume (1 < p < +∞) and Gardner et al [9] defined, as a generalization of L p -mixed volumes, the Orlicz mixed volumes. Orlicz mixed volumes now are main topics in the so-called Orlicz-Brunn-Minkowski theory proposed by Lutwak et al [25,26] (see also [17,18,36]). …”

Section: Introductionmentioning

confidence: 97%

Mixed volumes and measures of asymmetry

Jin

Leng

Guo

2014

Acta. Math. Sin.-English Ser.

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The mixed volume and the measure of asymmetry for convex bodies are two important topics in convex geometry. In this paper, we first reveal a close connection between the L p -mixed volumes proposed by E. Lutwak and the p-measures of asymmetry, which have the Minkowski measure as a special case, introduced by Q. Guo. Then, a family of measures of asymmetry is defined in terms of the Orlicz mixed volumes introduced by R. J. Gardner, D. Hug and W. Weil recently, which is an extension of the p-measures.

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On the Orlicz Minkowski Problem for Polytopes

Cited by 107 publications

References 51 publications

Orlicz Mean Dual Affine Quermassintegrals

Orlicz Mean Dual Affine Quermassintegrals

The planar Orlicz Minkowski problem in the L1-sense

Mixed volumes and measures of asymmetry

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