We derive a Brunn-Minkowski-type inequality regarding the volume of the Minkowski sum of degenerate sets, namely, line sets. Let A 1 : : : A n be one dimensional sets of unit length, and v

The main purposes of this paper are to establish some new Brunn– Minkowski inequalities for width-integrals of mixed projection bodies and affine surface area of mixed bodies, together with their inverse forms.

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.

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.

Abstract This paper aims to consider the dual Brunn–Minkowski inequality for log-volume of star bodies, and equivalent Minkowski mixed log-volume.

Traditional themes of our study of the state, including cores, peripheries, boundaries, national identities, treaties and laws are important in our understanding of the virtual or cyberstate. These fluid, three and four-dimensional worlds, associated with speed, networks and the compression of tie and space, call for a renewed focus on contemporary topics facing a polycentric, internetconnected...

In this article, we introduce the concept of general Lp-mixed chord integral difference star bodies. Further, establish Brunn–Minkowski type, Aleksandrov–Fenchel type and cyclic inequalities for difference.