Results 21 to 30 of about 2,936 (172)
Boundary restricted Brunn–Minkowski inequalities
Communications in Contemporary Mathematics, 2023 In this paper, we explore questions regarding the Minkowski sum of the boundaries of convex sets. Motivated by a question suggested to us by V. Milman regarding the volume of [Formula: see text] where [Formula: see text] and [Formula: see text] are convex bodies, we prove sharp volumetric lower bounds for the Minkowski average of the boundaries of ...
Shiri Artstein-Avidan +2 more
openaire +3 more sources
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
doaj +1 more source
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
wiley +1 more source
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
wiley +1 more source
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
wiley +1 more source
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
wiley +1 more source
Gaussian Brunn-Minkowski inequalities [PDF]
Transactions of the American Mathematical Society, 2010 This paper focuses on two fundamental ingredients of mathematics: Gauss measure \(\gamma_n\), the most important probability measure in \(\mathbb{R}^n\), and the Brunn-Minkowski inequality, one of the most powerful inequalities in analysis and geometry.
Gardner, Richard J., Zvavitch, Artem
openaire +1 more source
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
wiley +1 more source
Discrete variants of Brunn–Minkowski type inequalities [PDF]
Annales de la Faculté des sciences de Toulouse : Mathématiques, 2021 We present an alternative, short proof of a recent discrete version of the Brunn–Minkowski inequality due to Lehec and the second named author. Our proof also yields the four functions theorem of Ahlswede and Daykin as well as some new variants.
Halikias, Diana +2 more
openaire +3 more sources
Lp‐Curvature Measures and Lp,q‐Mixed Volumes
Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022 Motivated by Lutwak et al.’s Lp‐dual curvature measures, we introduce the concept of Lp‐curvature measures. This new Lp‐curvature measure is an extension of the classical surface area measure, Lp‐surface area measure, and curvature measure. In this paper, we first prove some properties of the Lp‐curvature measure.
Tongyi Ma, Raúl E. Curto
wiley +1 more source