Results 1 to 10 of about 87 (85)
The Functional Orlicz Brunn-Minkowski Inequality for q-Capacity
Journal of Function Spaces, 2020 In this paper, we establish functional forms of the Orlicz Brunn-Minkowski inequality and the Orlicz-Minkowski inequality for the electrostatic q-capacity, which generalize previous results by Zou and Xiong.
Wei Wang, Juan Li, Rigao He, Lijuan Liu
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On p-radial Blaschke and harmonic Blaschke additions [PDF]
Journal of Inequalities and Applications, 2017 In the paper, we first improve the radial Blaschke and harmonic Blaschke additions and introduce the p-radial Blaschke and p-harmonic Blaschke additions.
Chang-Jian Zhao
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Lp-dual three mixed quermassintegrals
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021 In the paper, the concept of Lp-dual three-mixed quermassintegrals is introduced. The formula for the Lp-dual three-mixed quermassintegrals with respect to the p-radial addition is proved. Inequalities of Lp-Minkowski, and Brunn-Minkowski type for the Lp-
Zhao Chang-Jian, Bencze Mihály
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The dual Brunn–Minkowski inequality for log-volume of star bodies
Journal of Inequalities and Applications, 2021 This paper aims to consider the dual Brunn–Minkowski inequality for log-volume of star bodies, and the equivalent Minkowski inequality for mixed log-volume.
Dandan Lai, Hailin Jin
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Entropic exercises around the Kneser–Poulsen conjecture
Mathematika, Volume 69, Issue 3, Page 841-866, July 2023., 2023 Abstract We develop an information‐theoretic approach to study the Kneser–Poulsen conjecture in discrete geometry. This leads us to a broad question regarding whether Rényi entropies of independent sums decrease when one of the summands is contracted by a 1‐Lipschitz map. We answer this question affirmatively in various cases.
Gautam Aishwarya +4 more
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Affine subspace concentration conditions for centered polytopes
Mathematika, Volume 69, Issue 2, Page 458-472, April 2023., 2023 Abstract Recently, K.‐Y. Wu introduced affine subspace concentration conditions for the cone volumes of polytopes and proved that the cone volumes of centered, reflexive, smooth lattice polytopes satisfy these conditions. We extend the result to arbitrary centered polytopes.
Ansgar Freyer +2 more
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On a geometric combination of functions related to Prékopa–Leindler inequality
Mathematika, Volume 69, Issue 2, Page 482-507, April 2023., 2023 Abstract We introduce a new operation between nonnegative integrable functions on Rn$\mathbb {R}^n$, that we call geometric combination; it is obtained via a mass transportation approach, playing with inverse distribution functions. The main feature of this operation is that the Lebesgue integral of the geometric combination equals the geometric mean ...
Graziano Crasta, Ilaria Fragalà
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General measure extensions of projection bodies
Proceedings of the London Mathematical Society, Volume 125, Issue 5, Page 1083-1129, November 2022., 2022 Abstract The inequalities of Petty and Zhang are affine isoperimetric‐type inequalities providing sharp bounds for Volnn−1(K)Voln(Π∘K)$\text{\rm Vol}^{n-1}_{n}(K)\text{\rm Vol}_n(\Pi ^\circ K)$, where ΠK$\Pi K$ is a projection body of a convex body K$K$.
Dylan Langharst +2 more
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A Steiner Inequality for the Anisotropic Perimeter
Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022 In this paper, we prove the monotonicity of the anisotropic perimeter of sets of finite perimeter under Steiner symmetrization by a variational formula of volume and an inequality for the anisotropic lower outer Minkowski content. As a consequence, we give a more direct proof of the Wulff inequality by Steiner symmetrization.
Jin Dai, Serena Matucci
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Inequalities for pqth-dual mixed volumes
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2023 In the paper, our main aim is to generalize the qth dual volume to Lp space, and introduce pqth-dual mixed volume by calculating the first order variation of qth dual volumes.
Zhao Chang-Jian, Bencze Mihály
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