Dual Orlicz-Brunn-Minkowski theory: dual Orlicz $L_{\phi}$ affine and geominimal surface areas

TL;DR

This paper develops the dual Orlicz $L_{}$ affine and geominimal surface areas for star bodies, establishing their fundamental properties and related inequalities within the dual Orlicz-Brunn-Minkowski framework.

Contribution

It introduces the dual Orlicz $L_{}$ affine and geominimal surface areas for star bodies and proves key inequalities, advancing the dual Orlicz-Brunn-Minkowski theory.

Findings

Established basic properties of the dual Orlicz $L_{}$ affine and geominimal surface areas.

Proved Orlicz affine isoperimetric, cyclic, Santalf3 style, and Alexander-Fenchel type inequalities.

Extended the dual Orlicz-Brunn-Minkowski theory for star bodies.

Abstract

This paper aims to develop basic theory for the dual Orlicz $L_{\phi}$ affine and geominimal surface areas for star bodies, which belong to the recent dual Orlicz-Brunn-Minkowski theory for star bodies. Basic properties for these new affine invariants will be provided. Moreover, related Orlicz affine isoperimetric inequality, cyclic inequality, Santal\'{o} style inequality and Alexander-Fenchel type inequality are established.