Orlicz hormonic Blaschke addition
Abstract
Recently, Gardner, Hug and Weil have introduced the Orlicz-Brunn-Minkowski theory: a general framework, additions, and inequalities. Following this, in the paper we consider Orlicz dual Brunn-Minkowski theory. We introduce Orlicz hormonic Blaschke addition which is an extension of the Lp hormonic Blaschke addition and L p radial Minkowski addition, respectively. Inequalities of dual Minkowski and Brunn-Minkowski type are obtained for the Orlicz hormonic Blaschke addition. The new Orlicz dual Brunn-Minkowski inequality implies the dual and L p -dual Brunn-Minkowski inequalities, respectively. New Orlicz dual Minkowski inequality implies the L p -dual Minkowski inequality. One of these has connections with the conjectured log-Brunn-Minkowski inequality of Lutwak, Yang, and Zhang, and in fact we show a log dual Minkowski inequality. Finally, we introduce the concept of Orlicz dual projection body and an inequality similar to Orlicz projection body is established.
Cite
@article{arxiv.2108.07724,
title = {Orlicz hormonic Blaschke addition},
author = {Chang-Jian Zhao},
journal= {arXiv preprint arXiv:2108.07724},
year = {2021}
}