The dual Orlicz-Aleksandrov-Fenchel inequality
Metric Geometry
2020-02-27 v1
Abstract
By calculating the first order variation of the dual mixed volumes, we put forward a new concept Orlicz multiple dual mixed volumes. The classical dual mixed volumes and dual Aleksandrov-Fenchel inequality are generalized to the Orlicz space. We establish dual Orlicz Aleksandrov-Fenchel inequality and a new concept of Lp multiple dual mixed volume and Lp dual Aleksandrov Fenchel inequality are first derived here, too. The dual Aleksandrov-Fenchel inequality and the Lp-dual Aleksandrov-Fenchel inequality are all special cases of the dual Orlicz-Aleksandrov-Fenchel inequality. As an application, a new dual Orlicz-Brunn-Minkowski inequality for the Orlicz harmonic addition is also established.
Keywords
Cite
@article{arxiv.2002.11112,
title = {The dual Orlicz-Aleksandrov-Fenchel inequality},
author = {Chang-Jian Zhao},
journal= {arXiv preprint arXiv:2002.11112},
year = {2020}
}