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arXiv · 2002.11112

The dual Orlicz-Aleksandrov-Fenchel inequality

Chang-Jian Zhao
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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.

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Chang-Jian Zhao. 2020-02-25. The dual Orlicz-Aleksandrov-Fenchel inequality. https://arxiv.org/abs/2002.11112

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