2020/02/25 by Chang-Jian Zhao, Zhao, Chang-Jian
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #FOS: Mathematics #Mathematical Inequalities and Applications #Metric Geometry (math.MG) #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.2002.11112
openalex publication_date 2020/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.