Supersymmetric Minkowski vacua in IIB orientifold compactifications based on orbifolds with background fluxes and non-perturbative superpotentials are investigated. Especially, microscopic requirements and difficulties to obtain such vacua are discussed. We show that orbifold models with one and two complex structure moduli and supersymmetric 2-form flux can be successfully stabilized to such v...

We compare the yields of two methods to obtain Bernstein type pointwise estimates for the derivative of a multivariate polynomial in points of some domain, where the polynomial is assumed to have sup norm at most 1. One method, due to Sarantopoulos, relies on inscribing ellipses into the convex domain K. The other, pluripotential theoretic approach, mainly due to Baran, works for even more gene...

It is well-known that the classical univariate orthogonal polynomials give rise to highly efficient Gaussian quadrature rules. We show how these classical families of polynomials can be generalized to a multivariate setting and how this generalization leads to truly Gaussian cubature rules for specific families of multivariate polynomials. The multivariate homogeneous orthogonal functions that ...

Then Xc is the completion of {X, \\ \\c). Alternatively || ||c is the Minkowski functional of the convex hull of the unit ball. Xc has the property that any bounded linear operator L:X —> Z into a Banach space extends with preservation of norm to an operator L\XC —» Z. The Banach envelope of / (0 < p < 1) is, of course, lx. In 1969, Duren, Romberg and Shields [3] identified the dual space of H_...

The topology of the Las Campanas Redshift Survey is analyzed using Minkowski functional statistics, taking into account the selection effects of the survey. The results are compared with the predictions of some toy models of structure formation, including the Standard Cold Dark Matter Model and topological defect-based models. All of the toy models have a scale invariant primordial spectrum of ...

A class < of convex bodies (c-bodies) P,Q, . . . in a k-dimensional Euclidean space R is called convex, when for all P,Q ∈ < always follows αP × βQ ∈ < [α, β ≥ 0, α+ β = 1]. Here we interpret λP (with λ > 0) to be a c-body, obtained from P through a dilatation with respect to a fixed originO of the spaceR; P ×Q refers to Minkowski addition. This property of a class of c-bodies thus not only ref...

The classical Minkowski problem lead to the Lp Minkowski problem and now to the Orlicz-Minkowski problem. Existence is demonstrated for the even Orlicz-Minkowski problem. A byproduct is a new approach to the solution of the classical Minkowski problem.

This paper is devoted to establishing some functional generalizations of Hölder and reverse Hölder’s inequalities with local fractional integral introduced by Yang. Then, based on the obtained results, we derive related including Minkowski-type Dresher-type inequalities, which are extensions several existing inequalities.

The Brunn–Minkowski inequality gives a lower bound of the Lebesgue measure of a sum-set in terms of the measures of the individual sets. It has played a crucial role in the theory of convex bodies. This topic has many interactions with isoperimetry or functional analysis. Our aim here is to report some recent aspects of these interactions involving optimal mass transport or the Heat equation. A...