Affine isoperimetric inequalities in the functional Orlicz-Brunn-Minkowski theory

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• 作者：Umut Caglar^a ; ^{ucaglar@fiu.edu" class="auth_mail" title="E-mail the corresponding author} ; Deping Ye^b ; ^{deping.ye@mun.ca" class="auth_mail" title="E-mail the corresponding author}
• 关键词：52A20 ; 53A15 ; 46B ; 60B
• 刊名：Advances in Applied Mathematics
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：81
• 期：Complete
• 页码：78-114
• 全文大小：586 K

文摘

In this paper, we develop a basic theory of Orlicz affine and geominimal surface areas for convex and s-concave functions. We prove some basic properties for these newly introduced functional affine invariants and establish related functional affine isoperimetric inequalities as well as functional Santaló type inequalities.