This is an announcement for the paper "Dual Orlicz-Brunn-Minkowski theory: dual Orlicz $L_{\phi}$ affine and geominimal surface areas" by Deping Ye.
Abstract: This paper aims to develop basic theory for the dual Orlicz $L_{\phi}$ affine and geominimal surface areas for star bodies, which are dual to the Orlicz $L_{\phi}$ affine and geominimal surface areas for convex bodies (Ye, arXiv:1403.1643). These new affine invariants belong to the recent dual Orlicz-Brunn-Minkowski theory for star bodies (Ye, arXiv:1404.6991). 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. Besides, an Orlicz isoperimetric inequality for the Orlicz $\phi$-surface area and an Orlicz-Urysohn inequality for the Orlicz $\phi$ mean width are given.
Archive classification: math.MG math.DG math.FA
Mathematics Subject Classification: 52A20, 53A15
Submitted from: deping.ye@gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1405.0746
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