Abstract of a paper by Deping Ye
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 or http://arXiv.org/abs/1405.0746
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alspach@math.okstate.edu