Related papers: Some inequalities for tetrahedra
Matrix versions of some basic convexity inequalities are given. Further results on the same topic are proved in the recent papers on arxiv: 1. Hermitian operators and convex functions, 2. A concavity inequality for symmetric norms, 3.…
In this note, we improve Nikulin's inequality in the case of right-angled hyperbolic polyhedra. The new inequality allows to give much shorter proofs of the known dimension bounds. We also improve Nonaka's lower bound on the number of ideal…
On real hypersurfaces in complex space forms many results are proven. In this paper we generalize some results concerning extrinsic geometry of real hypersurfaces, to CR submanifolds of maximal CR dimension in complex space forms.
In this paper we prove some new symmetry results for the extremals of the Caffarelli-Kohn-Nirenberg inequalities, in any dimension larger or equal than two.
A stability version of the reverse isoperimetric inequality, and the corresponding inequality for isotropic measures are established.
We prove integral curvature bounds in terms of the Betti numbers for compact submanifolds of the Euclidean space with low codimension. As an application, we obtain topological obstructions for $\delta$-pinched immersions. Furthermore, we…
We give an expression for a generalized numerical radius of Hilbert space operators and then apply it to obtain upper and lower bounds for the generalized numerical radius. We also establish some generalized numerical radius inequalities…
We offer new proofs, refinements as well as new results related to classical means of two variables, including the identric and logarithmic means.
Some new reverses for the generalised triangle inequality in inner product spaces and applications are given. Applications in connection to the Schwarz inequality are provided as well.
We discuss certain ternary algebraic structures appearing more or less naturally in various domains of theoretical and mathematical physics. Far from being exhaustive, this article is intended above all to draw attention to these algebras,…
We study the general rational trigonometry of a tetrahedron, based on quadrances, spreads and solid spreads, using vector products associated to an arbitrary symmetric bilinear form over a general field, not of characteristic two. This…
We prove that there are "many" non-congruent tetrahedra in the truncated lattice $[0,q]^3\cap \mathbb{Z}^3$.
We obtain simple proofs of certain inequalites for bivariate means.
We settle the case of equality for the relative isoperimetric inequality outside any arbitrary convex set with not empty interior.
The main purpose of this paper is to prove a sharp Sobolev inequality in an exterior of a convex bounded domain. There are two ingredients in the proof: One is the observation of some new isoperimetric inequalities with partial free…
We show that an inequality related to Newton's inequality provides one more relation between skewness and kurtosis. This also gives simple and alternative proofs of the bounds for skewness and kurtosis.
This article is concerned with the approximation of unbounded convex sets by polyhedra. While there is an abundance of literature investigating this task for compact sets, results on the unbounded case are scarce. We first point out the…
We prove a trace Hardy type inequality with the best constant on the polyhedral convex cones which generalizes recent results of Alvino et al. and of Tzirakis on the upper half space. We also prove some trace Hardy-Sobolev-Maz'ya type…
The paper is devoted to some extremal problems, related to convex polygons in the Euclidean plane and their perimeters. We present a number of results that have simple formulations, but rather intricate proofs. Related and still unsolved…
We study inequalities between the hyperbolic metric and intrinsic metrics in convex polygonal domains in the complex plane. Special attention is paid to the triangular ratio metric in rectangles. A local study leads to an investigation of…