Results 1 to 10 of about 34 (34)
Isoperimetric and Brunn-Minkowski inequalities for the (p, q)-mixed geominimal surface areas
Open Mathematics, 2022 Motivated by the celebrated work of Lutwak, Yang and Zhang [1] on (p,q)\left(p,q)-mixed volumes and that of Feng and He [2] on (p,q)\left(p,q)-mixed geominimal surface areas, we in the present paper establish and confirm the affine isoperimetric and ...
Zhang Juan, Wang Weidong, Zhao Peibiao
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Some inequalities for star duality of the radial Blaschke-Minkowski homomorphisms
Open Mathematics, 2020 In 2006, Schuster introduced the radial Blaschke-Minkowski homomorphisms. In this article, associating with the star duality of star bodies and dual quermassintegrals, we establish Brunn-Minkowski inequalities and monotonic inequality for the radial ...
Zhao Xia, Wang Weidong, Lin Youjiang
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Iterations of the projection body operator and a remark on Petty’s conjectured projection inequality [PDF]
, 2018 Mathematics subject classification; 52A20, 53A15, 52A39 ...
Saroglou, Christos, Zvavitch, Artem
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Open Mathematics, 2018 In this paper, by the Orlicz-Minkowski combinations of convex bodies, we define the general Orlicz difference bodies and study their properties. Furthermore, we obtain the extreme values of the general Orlicz difference bodies and their polars.
Shi Wei, Wang Weidong, Ma Tongyi
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Forum of Mathematics, SigmaA spectral convex set is a collection of symmetric matrices whose range of eigenvalues forms a symmetric convex set. Spectral convex sets generalize the Schur-Horn orbitopes studied by Sanyal–Sottile–Sturmfels (2011). We study this class of convex bodies,
Raman Sanyal, James Saunderson
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Lorentzian polynomials on cones
Forum of Mathematics, SigmaInspired by the theory of hyperbolic polynomials and Hodge theory, we develop the theory of Lorentzian polynomials on cones. This notion captures the Hodge-Riemann relations of degree zero and one.
Petter Brändén, Jonathan Leake
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Equality cases of the Alexandrov–Fenchel inequality are not in the polynomial hierarchy
Forum of Mathematics, PiDescribing the equality conditions of the Alexandrov–Fenchel inequality [Ale37] has been a major open problem for decades. We prove that in the case of convex polytopes, this description is not in the polynomial hierarchy unless the polynomial hierarchy ...
Swee Hong Chan, Igor Pak
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Geometric properties of the family of p-parallel bodies
Analysis and Geometry in Metric SpacesWe study geometric properties of the family of p-parallel bodies of a convex body K with respect to a gauge body E. In particular, we investigate various regularity properties of their boundaries by means of their 0-extreme vectors, aiming for extensions
Hernández Cifre María A. +2 more
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Some inequalities for Lp radial Blaschke-Minkowski homomorphisms1
, 2019 The notion of radial Blaschke-Minkowski homomorphisms was presented by Schuster. Afterwards, Wang et al. introduced Lp radial Blaschke-Minkowski homomorphisms.
Wang, Weidong, Chen, Bin
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, 1997 Polyhedral homotopy continuation methods exploit the sparsity of polynomial systems so that the number of solution curves to reach all isolated solutions is optimal for generic systems.
Jan Verschelde +3 more
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