Inequalities for pqth-dual mixed volumes

Abstract

In the paper, our main aim is to generalize the qth dual volume to Lp space, and introduce pqth-dual mixed volume by calculating the first order variation of qth dual volumes. We establish the Lpq-Minkowski inequality for pqth-dual mixed volumes and Lpq-Brunn-Minkowski inequality for the qth-dual volumes, respectively. The new inequalities in special case yield some new dual inequalities for the qth-dual volumes.

Keywords

• log-volume
• qth dual volume
• qth-dual mixed volume
• pqth-dual mixed volume
• primary 46e30
• secondary 52a40