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

Abstract

This paper aims to develop basic theory for the dual Orlicz $L_{\varphi }$ 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, Santaló style inequality and Alexander-Fenchel type inequality are established.

Some changes are made in this version. The Orlicz $L_{\varphi }$-dual mixed volume defined in arXiv:1407.7311 (instead of arXiv:1404.6991) is used to define the dual Orlicz $L_{\varphi }$ affine and geominimal surface areas. Moreover, the proofs are simplified

References in corpus (8)

• General affine surface areas
• Relative entropy of cone measures and $L_p$ centroid bodies
• General Lp affine isoperimetric inequalities
• The Dual Orlicz-Brunn-Minkowski Theory
• New Orlicz Affine Isoperimetric Inequalities
• The mixed $L_p$ geominimal surface areas for multiple convex bodies
• Inequalities for general mixed affine surface areas
• On the monotone properties of general affine surface areas under the Steiner symmetrization

Cited by in corpus (7)

• The Dual Orlicz-Brunn-Minkowski Theory
• The dual Orlicz-Minkowski problem
• On the general dual Orlicz-Minkowski problem
• The $p$-capacitary Orlicz-Hadamard variational formula and Orlicz-Minkowski problems
• The dual Orlicz-Aleksandrov-Fenchel inequality
• An affine Orlicz Polya-Szego principle
• Orlicz version of the mixed width integrals