English

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}
}