In this paper, we prove the monotonicity of anisotropic perimeter sets finite under Steiner symmetrization by a variational formula volume and an inequality for lower outer Minkowski content. As consequence, give more direct proof Wulff symmetrization.

In this paper, we introduce a new concept of volumes difference function of the projection and intersection bodies. Following this, we establish the Minkowski and Brunn-Minkowski inequalities for volumes difference function of the projection and intersection bodies.

We prove the following isoperimetric type inequality: Given a finite absolutely continuous Borel measure on ${\mathbb R}^n$, halfspaces have maximal among all subsets with prescribed barycenter. As consequence, we make progress towards solution to problem of Henk and Pollehn, which is equivalent Log-Minkowski inequality for parallelotope centered convex body. Our probabilistic approach also giv...

Basic properties of finite subsets of the integer lattice Z are investigated from the point of view of geometric tomography. Results obtained concern the Minkowski addition of convex lattice sets and polyominoes, discrete X-rays and the discrete and continuous covariogram, the determination of symmetric convex lattice sets from the cardinality of their projections on hyperplanes, and a discrete...

In this research, we introduce some new fractional integral inequalities of Minkowski’s type by using Riemann-Liouville operator. We replace the constants that appear on inequality two positive functions. Further, establish related to reverse Minkowski via integral. Using operator, special cases are also discussed.

In this paper, we study spatially homogeneous solutions of the Boltzmann equation in special relativity and in Robertson-Walker spacetimes. We obtain an analogue of the Povzner inequality in the relativistic case and use it to prove global existence theorems. We show that global solutions exist for a certain class of collision cross sections of the hard potential type in Minkowski space and in ...

In the paper, a nonconvex quasidifferentiable optimization problem with the inequality constraints is considered. The concept of a univex function with respect to a convex compact set is introduced. Further, the sufficient optimality conditions and several duality results in the sense of Mond-Weir are established for the considered quasidifferentiable optimization problem under assumption that ...

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...