Abstract of a paper by Deping Ye
This is an announcement for the paper "Dual Orlicz-Brunn-Minkowski theory: Orlicz $\varphi$-radial addition, Orlicz $L_{\phi}$-dual mixed volume and related inequalities" by Deping Ye. Abstract: This paper develops basic setting for the dual Orlicz-Brunn-Minkowski theory for star bodies. An Orlicz $\varphi$-radial addition of two or more star bodies is proposed and related dual Orlicz-Brunn-Minkowski inequality is established. Based on a linear Orlicz $\varphi$-radial addition of two star bodies, we derive a formula for the Orlicz $L_{\phi}$-dual mixed volume. Moreover, a dual Orlicz-Minkowski inequality for the Orlicz $L_{\phi}$-dual mixed volume, a dual Orlicz isoperimetric inequality for the Orlicz $L_{\phi}$-dual surface area and a dual Orlicz-Urysohn inequality for the Orlicz $L_{\phi}$-harmonic mean radius are proved. 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/1404.6991 or http://arXiv.org/abs/1404.6991
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alspach@math.okstate.edu