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Extremal general affine surface areas
Journal of Mathematical Analysis and Applications ( IF 1.2 ) Pub Date : 2021-07-19 , DOI: 10.1016/j.jmaa.2021.125506
Steven Hoehner 1
Affiliation  

For a convex body K in Rn, we introduce and study the extremal general affine surface areas, defined byISφ(K):=supKKasφ(K),osψ(K):=infKKasψ(K) where asφ(K) and asψ(K) are the Lφ and Lψ affine surface area of K, respectively. We prove that there exist extremal convex bodies that achieve the supremum and infimum, and that the functionals ISφ and osψ are continuous. In our main results, we prove Blaschke-Santaló type inequalities and inverse Santaló type inequalities for the extremal general affine surface areas. This article may be regarded as an Orlicz extension of the recent work of Giladi, Huang, Schütt and Werner (2020), who introduced and studied the extremal Lp affine surface areas.



中文翻译:

极值一般仿射表面积

对于凸体K in电阻n,我们介绍和研究极值一般仿射表面积,定义为φ()=作为φ(),操作系统ψ()=信息作为ψ() 在哪里 作为φ()作为ψ()φψ分别为K 的仿射表面积。我们证明存在达到上界和下界的极值凸体,并且泛函φ操作系统ψ是连续的。在我们的主要结果中,我们证明了极值一般仿射表面积的 Blaschke-Santaló 型不等式和逆 Santaló 型不等式。这篇文章可以看作是 Giladi、Huang、Schütt 和 Werner (2020) 近期工作的 Orlicz 延伸,他们介绍并研究了极值 仿射表面积。

更新日期:2021-07-27
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