in this paper, two pairs of new inequalities are given, which decompose two hilbert-type inequalities.

For 0 < p < 1, Haberl and Ludwig defined the notions of symmetric and asymmetric Lp-intersection bodies. Recently, Wang and Li introduced the general Lp-intersection bodies. In this paper, we give the Lp-dual geominimal surface area forms for the extremum values and Brunn-Minkowski type inequality of general Lp-intersection bodies. Further, combining with the Lp-dual geominimal surface areas, w...

For a general family of graphs on Zn, we translate the edge-isoperimetric problem into a continuous isoperimetric problem in Rn. We then solve the continuous isoperimetric problem using the Brunn-Minkowski inequality and Minkowski’s theorem on mixed volumes. This translation allows us to conclude, under a reasonable assumption about the discrete problem, that the shapes of the optimal sets in t...

In this paper we have shall generalize Shearer’s entropy inequality and its recent extensions by Madiman and Tetali, and shall apply projection inequalities to deduce extensions of some of the inequalities concerning sums of sets of integers proved recently by Gyarmati, Matolcsi and Ruzsa. We shall also discuss projection and entropy inequalities and their connections.

In this paper, we construct an injection A × B → M ×M from the product of any two nonempty subsets of the symmetric group into the square of their midpoint set, where the metric is that corresponding to the conjugacy class of transpositions. If A and B are disjoint, our construction allows to inject two copies of A × B into M ×M . These injections imply a positively curved Brunn-Minkowski inequ...

We outline existence of the Brenier map. As an application we present simple proofs of the multiplicative form of the Brunn–Minkowski inequality and the Marton–Talagrand inequality. 1.