2021/08/11 by Chang-Jian Zhao, Zhao, Chang-Jian
Mathematics · #FOS: Mathematics #General Mathematics (math.GM) #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.2108.07724
openalex publication_date 2021/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recently, Gardner, Hug and Weil have introduced the Orlicz-Brunn-Minkowski theory: a general framework, additions, and inequalities. Following this, in the paper we consider Orlicz dual Brunn-Minkowski theory. We introduce Orlicz hormonic Blaschke addition which is an extension of the Lp hormonic Blaschke addition and L p radial Minkowski addition, respectively. Inequalities of dual Minkowski and Brunn-Minkowski type are obtained for the Orlicz hormonic Blaschke addition. The new Orlicz dual Brunn-Minkowski inequality implies the dual and L p -dual Brunn-Minkowski inequalities, respectively. New Orlicz dual Minkowski inequality implies the L p -dual Minkowski inequality. One of these has connections with the conjectured log-Brunn-Minkowski inequality of Lutwak, Yang, and Zhang, and in fact we show a log dual Minkowski inequality. Finally, we introduce the concept of Orlicz dual projection body and an inequality similar to Orlicz projection body is established.