Related papers: Minkowski's inequality and sums of squares

Certain excess versions of the Minkowski and H\"older inequalities are given. These new results generalize and improve the Minkowski and H\"older inequalities.

We generalize the classical Minkowski integral inequality to the form involving general Banach function norms.

We obtain inequalities of H\"{o}lder and Minkowski type with weights generalizing both the case of weights with alternating signs and the classical case of non-negative weights.

In this exposition of the equality and inequality of Minkowski for multiplicity of ideals, we provide simple algebraic and geometric proofs. Connections with mixed multiplicities of ideals are explained.

The mixed-norm versions of the H\"older and Minkowski integral inequalities are used to produce new, general estimates involving symmetric geometric means of mixed norms. Various existing mixed-norm estimates are shown to be simple special…

The relationship between nonnegative polynomials and sums of squares is one of the central questions in real algebraic geometry. A modern approach is to look at nonnegative polynomials and sums of squares on a real variety. We survey the…

Recent results about sums of cubes of Fibonacci numbers [Frontczak, 2018] are extended to arbitrary powers.

Signed Minkowski decomposition is an expression of a polytope as a Minkowski sum and difference of smaller polytopes. Signed Minkowski decompositions of a polytope can be interpreted as factorizations of a max-plus (tropical) function. We…

We derive a general recurrence relation for squares of Fibonacci-like numbers. Various properties are developed, including double binomial summation identites.

A quantitative version of Minkowski sum, extending the definition of $\theta$-convolution of convex bodies, is studied to obtain extensions of the Brunn-Minkowski and Zhang inequalities, as well as, other interesting properties on Convex…

In pioneering works of Meyer and of McMullen in the early 1970s, the set of Minkowski summands of a polytope was shown to be a polyhedral cone called the type cone. Explicit computations of type cones are in general intractable.…

We refine and extend quantitative bounds, on the fraction of nonnegative polynomials that are sums of squares, to the multihomogenous case.

The classical Minkowski inequality implies that the volume of a bounded convex domain is controlled from above by the integral of the mean curvature of its boundary. In this note, we establish an analogous inequality without the convexity…

In this study, we obtain some new integral inequalities for different classes of convex functions by using some elementary inequalities and classical inequalities like general Cauchy inequality and Minkowski inequality.

We characterize all signed Minkowski sums that define generalized permutahedra, extending results of Ardila-Benedetti-Doker (2010). We use this characterization to give a complete classification of all positive, translation-invariant,…

In this paper, we discuss the toric ideals of Minkowski sums of unit simplices. More precisely, we prove that the toric ideal of Minkowski sum of unit simplices has a squarefree initial ideal and is generated by quadratic binomials.…

A generalization of the classical Lipschitz summation formula is proposed. It involves new polylogarithmic rational functions constructed via the Fourier expansion of certain sequences of Bernoulli--type polynomials. Related families of…

Some inequalities and reverses of classic H\"{o}lder and Minkowski types are obtained for scalar Birkhoff weak integrable functions with respect to a non-additive measure.

Minkowski sums are of theoretical interest and have applications in fields related to industrial backgrounds. In this paper we focus on the specific case of summing polytopes as we want to solve the tolerance analysis problem described in…

In this paper, we derive a formula for the sums of powers of the first $n$ positive integers, $S_k(n)$, that involves the hyperharmonic numbers and the Stirling numbers of the second kind. Then, using an explicit representation for the…