Results 11 to 20 of about 73 (58)
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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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
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Strengthened inequalities for the mean width and the ℓ‐norm
Journal of the London Mathematical Society, Volume 104, Issue 1, Page 233-268, July 2021., 2021 Abstract Barthe proved that the regular simplex maximizes the mean width of convex bodies whose John ellipsoid (maximal volume ellipsoid contained in the body) is the Euclidean unit ball; or equivalently, the regular simplex maximizes the ℓ‐norm of convex bodies whose Löwner ellipsoid (minimal volume ellipsoid containing the body) is the Euclidean unit
Károly J. Böröczky +2 more
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INEQUALITIES BETWEEN MIXED VOLUMES OF CONVEX BODIES: VOLUME BOUNDS FOR THE MINKOWSKI SUM
Mathematika, Volume 66, Issue 4, Page 1003-1027, October 2020., 2020 Abstract In the course of classifying generic sparse polynomial systems which are solvable in radicals, Esterov recently showed that the volume of the Minkowski sum P1+⋯+Pd of d‐dimensional lattice polytopes is bounded from above by a function of order O(m2d), where m is the mixed volume of the tuple (P1,⋯,Pd).
Gennadiy Averkov +2 more
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The Schur Multiplicative and Harmonic Convexities for Three Classes of Symmetric Functions
Journal of Function Spaces, Volume 2018, Issue 1, 2018., 2018 We investigate the Schur harmonic convexity for two classes of symmetric functions and the Schur multiplicative convexity for a class of symmetric functions by using a new method and generalizing previous result. As applications, we establish some inequalities by use of the theory of majorization, in particular, and we give some new geometric ...
Ming-bao Sun +4 more
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Computing the Discrete Compactness of Orthogonal Pseudo‐Polytopes via Their nD‐EVM Representation
Mathematical Problems in Engineering, Volume 2010, Issue 1, 2010., 2010 This work is devoted to present a methodology for the computation of Discrete Compactness in n‐dimensional orthogonal pseudo‐polytopes. The proposed procedures take in account compactness′ definitions originally presented for the 2D and 3D cases and extend them directly for considering the nD case.
Ricardo Pérez-Aguila, Mohammad Younis
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New fiber and graph combinations of convex bodies
Mathematika, Volume 71, Issue 4, October 2025.Abstract Three new combinations of convex bodies are introduced and studied: the Lp$L_p$ fiber, Lp$L_p$ chord, and graph combinations. These combinations are defined in terms of the fibers and graphs of pairs of convex bodies, and each operation generalizes the classical Steiner symmetral, albeit in different ways.
Steven Hoehner, Sudan Xing
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Geometric inequalities, stability results and Kendall's problem in spherical space
Mathematika, Volume 71, Issue 4, October 2025.Abstract In Euclidean space, the asymptotic shape of large cells in various types of Poisson‐driven random tessellations has been the subject of a famous conjecture due to David Kendall. Since shape is a geometric concept and large cells are identified by means of geometric size functionals, the resolution of the conjecture is inevitably connected with
Daniel Hug, Andreas Reichenbacher
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Tightening inequalities on volume‐extremal k$k$‐ellipsoids using asymmetry measures
Mathematika, Volume 71, Issue 4, October 2025.Abstract We consider two well‐known problems: upper bounding the volume of lower dimensional ellipsoids contained in convex bodies given their John ellipsoid, and lower bounding the volume of ellipsoids containing projections of convex bodies given their Loewner ellipsoid.
René Brandenberg, Florian Grundbacher
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On profinite rigidity amongst free‐by‐cyclic groups I: The generic case
Proceedings of the London Mathematical Society, Volume 130, Issue 6, June 2025.Abstract We prove that amongst the class of free‐by‐cyclic groups, Gromov hyperbolicity is an invariant of the profinite completion. We show that whenever G$G$ is a free‐by‐cyclic group with first Betti number equal to one, and H$H$ is a free‐by‐cyclic group which is profinitely isomorphic to G$G$, the ranks of the fibres and the characteristic ...
Sam Hughes, Monika Kudlinska
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