Results 31 to 40 of about 671 (71)

On Minkowski's inequality and its application

Journal of Inequalities and Applications, 2011
In the paper, we first give an improvement of Minkowski integral inequality. As an application, we get new Brunn-Minkowski-type inequalities for dual mixed volumes.
Cheung Wing-Sum, Zhao Chang-Jian
doaj  

The regularity of solutions to the Lp Gauss image problem

Open Mathematics
The Lp{L}_{p} Gauss image problem amounts to solving a class of Monge-Ampère type equations on the sphere. In this article, we discuss the regularity of solutions to the Lp{L}_{p} Gauss image problem.
Jia Xiumei, Chen Jing
doaj   +1 more source

Small holding circles

, 2011
A circle C holds a convex body K if C does not meet the interior of K and if there does not exist any euclidean displacement which moves C as far as desired from K, avoiding the interior of K.
Fruchard, Augustin
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Local minimality of the volume-product at the simplex

, 2010
It is proved that the simplex is a strict local minimum for the volume product, P(K)=min(vol(K) vol(K^z)), K^z is the polar body of K with respect to z, the minimum is taken over z in the interior of K, in the Banach-Mazur space of n-dimensional (classes
Gordon, Jaegil Kim, Klee, Mahler, Mahler, Santaló, Shlomo Reisner   +6 more
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On a Santaló point for Nakamura-Tsuji’s Laplace transform inequality

Forum of Mathematics, Sigma
Nakamura and Tsuji recently obtained an integral inequality involving a Laplace transform of even functions that implies, at the limit, the Blaschke-Santaló inequality in its functional form.
Dario Cordero-Erausquin, Matthieu Fradelizi, Dylan Langharst   +2 more
doaj   +1 more source

Lorentzian polynomials on cones

Forum of Mathematics, Sigma
Inspired 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
doaj   +1 more source

Equality cases of the Alexandrov–Fenchel inequality are not in the polynomial hierarchy

Forum of Mathematics, Pi
Describing 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
doaj   +1 more source

Inequalities of Aleksandrov body

Journal of Inequalities and Applications, 2011
A new concept of p-Aleksandrov body is firstly introduced. In this paper, p-Brunn-Minkowski inequality and p-Minkowski inequality on the p-Aleksandrov body are established.
Yan Hu, Junhua Jiang
doaj  

Geometric properties of the family of p-parallel bodies

Analysis and Geometry in Metric Spaces
We 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., Martínez Fernández Antonio R., Saorín Gómez Eugenia   +2 more
doaj   +1 more source

The Rosenthal-Szasz inequality for normed planes

, 2018
We aim to study the classical Rosenthal-Szasz inequality for a plane whose geometry is given by a norm. This inequality states that the bodies of constant width have the largest perimeter among all planar convex bodies of given diameter.
Balestro, Vitor, Martini, Horst
core