Related papers: Some inequalities for tetrahedra
In this paper weighted Dirichlet-type inequalities for the decreasing rearrangement in cylinders are proved. A weighted isoperimetric inequality is also obtained.
We prove sharp inequalities for the average number of affine diameters through the points of a convex body $K$ in ${\mathbb R}^n$. These inequalities hold if $K$ is either a polytope or of dimension two. An example shows that the proof…
In this work we study inside-out dissections of polygons and polyhedra. We first show that an arbitrary polygon can be inside-out dissected with $2n+1$ pieces, thereby improving the best previous upper bound of $4(n-2)$ pieces.…
In this paper, we study the symmetrized Talagrand inequality that was proved by Fathi and has a connection with the Blaschke-Santal\'{o} inequality in convex geometry. As corollaries of our results, we have several refined functional…
We prove several congruences for trinomial coefficients.
We present tight Bell inequalities expressed by probabilities for three four- and five-dimensional systems. The tight structure of Bell inequalities for three $d$-dimensional systems (qudits) is proposed. Some interesting Bell inequalities…
In this article we derive some polynomial inequalities for Mertens functions.
Often some interesting or simply curious points are left out when developing a theory. It seems that one of them is the existence of an upper bound for the fraction of area of a convex and closed plane area lying outside a circle with which…
We introduce different notions of polynomial convexity with bounds on degrees of polynomials in $\mathbb C^n$. We provide some examples in higher dimensions and show necessary and sufficient conditions for polynomial convexity with degree…
We present a refinement, by selfimprovement, of the arithmetic geometric inequality.
In this article, a series of new inequalities involving the $q$-numerical radius for $n\times n$ tridiagonal, and anti-tridiagonal operator matrices has been established. These inequalities serve to establish both lower and upper bounds for…
We prove several stability and volume difference inequalities for projections of convex bodies and apply them to prove a hyperplane inequality for surface area of projection bodies.
We prove that the orbit closure of the determinant is not normal. A similar result is obtained for the orbit closure of the permanent multiplied by a power of a linear form.
Gradients of the perimeter and area of a polygon have straightforward geometric interpretations. The use of optimality conditions for constrained problems and basic ideas in triangle geometry show that polygons with prescribed area…
In this paper we deal with the problem to find the maximal volume polyhedra with a prescribed property and inscribed in the unit sphere. We generalize those inequality (called by \emph{icosahedron inequality}) of L. Fejes-T\'oth of which an…
This is an example on the cohomology of threefolds.
In this paper, we study the integral curvatures of Finsler manifolds and prove several Myers type theorems.
Geodesic loops on polyhedra were studied only for Euclidean space and it was known that there are no simple geodesic loops on regular tetrahedra. Here we prove that: 1) On the spherical space, there are no simple geodesic loops on…
This paper is an introduction to Coxeter polyhedra in spherical, Euclidean, and hyperbolic geometries. It consists of essentially two parts that could be read independently. In the first we introduce non-obtuse polyhedra in the spherical,…
Some new Gruss type inequalities in inner product spaces and applications for integrals are given.