Affine isoperimetric inequalities in the functional Orlicz–Brunn–Minkowski theory

In this paper, we develop a basic theory of Orlicz affine and geominimal surface areas for convex and s-concave functions. We prove some basic properties for these newly introduced functional affine invariants and establish related functional affine isoperimetric inequalities as well as functional Santaló type inequalities.     

Geometric interpretation of hadronization model

A hadronization model termed as geometric dielectric confinement model is described. The model describes the charmed meson decays quite successfully. In the model we assume that the non-abelian gauge field describing the colour force simulates the effect of a medium having space-dependent dielectric constant. The quarks produced in weak decays move in the dielectric medium such that they are free in limited region of space (r⋍0) and cannot appear as asymptotic states resulting in hadronization. It is found that the dielectric medium resembles anti-desitter microuniverse and the quarks behave essentially as free particles damped by gaussian distribution. The model reproduces from a single Lagrangian the quark motion as well as the form of dielectric function.