The isoperimetric inequality for Steiner symmetrization of any codimension is investigated and the equality cases are characterized. Moreover, a quantitative version of this inequality is proven for convex sets.

We present an alternative, short proof of a recent discrete version the Brunn–Minkowski inequality due to Lehec and second named author. Our also yields four functions theorem Ahlswede Daykin as well some new variants.

The aim of this work is to obtain the reverse Minkowski integral inequality. For aim, we first give a proposition which important for our main results. Then establish some inequalities parameters 0 < p 1 and 0, respectively.

The Petty projection inequality for sets of finite perimeter is proved. Our approach based on Steiner symmetrization. Neither the affine Sobolev nor functional Minkowski problem used in our proof. Moreover, perimeter, we prove with respect to

In this paper we first introduce quermassintegrals for free boundary hypersurfaces in the $(n+1)$-dimensional Euclidean unit ball. Then solve some related isoperimetric type problems convex hypersurfaces, which lead to new Alexandrov–Fenchel inequalities. particular, $n = 2$ obtain a Minkowski-type inequality and 3$ an optimal Willmore-type inequality. To prove these estimates, employ specifica...