Results 21 to 30 of about 489,827 (153)
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 ...
Artstein-Avidan, Shiri +2 more
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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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On discrete $$L_p$$ Brunn–Minkowski type inequalities
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2022 Abstract$$L_p$$ L p Brunn–Minkowski type inequalities for the lattice point enumerator $$\mathrm {G}_n(\cdot )$$ G n
Hernandez Cifre, Maria A. +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
wiley +1 more source
The Brunn-Minkowski inequality and the Heisenberg group [PDF]
, 2023 openThe core of this thesis is the Brunn-Minkowski inequality. We start proving the general version of the Brunn-Minkowski inequality in the Euclidean space, then we investigate the validity of a "geodesic" version of the Brunn-Minkowski inequality in ...
BENETTON, GIOELE
core
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
An Expository Lecture of María Jesús Chasco on Some Applications of Fubini’s Theorem
Axioms, 2021 The usefulness of Fubini’s theorem as a measurement instrument is clearly understood from its multiple applications in Analysis, Convex Geometry, Statistics or Number Theory. This article is an expository paper based on a master class given by the second
Alberto Castejón +3 more
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The Orlicz Brunn–Minkowski inequality
Advances in Mathematics, 2014 The Orlicz-Brunn-Minkowski theory was introduced by Lutwak, Yang and Zhang, being an extension of the classical Brunn-Minkowski theory. It represents a generalization of the \(L_p\)-Brunn-Minkowski theory. For a convex, strictly increasing \(\phi:[0,\infty]\longrightarrow [0,\infty)\), with \(\phi(0)=0\) and \(K,L\) convex and compact sets containing ...
Xi, Dongmeng +2 more
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Cyclic Brunn–Minkowski inequalities for general width and chord-integrals
Journal of Inequalities and Applications, 2019 In this paper, we establish two cyclic Brunn–Minkowski inequalities for the general ith width-integrals and general ith chord-integrals, respectively. Our works bring the cyclic inequality and Brunn–Minkowski inequality together.
Linmei Yu, Yuanyuan Zhang, Weidong Wang
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On Discrete LOG-Brunn--Minkowski Type Inequalities
SIAM Journal on Discrete Mathematics, 2022 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hernández Cifre, María de los Ángeles +1 more
openaire +4 more sources