Lutwak-Petty projection inequalities for Minkowski valuations and their duals

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:490

Article

Berg, Astrid¹  Schuster, Franz E.¹ 

[1] Vienna Univ Technol, Vienna, Austria

关键词: Isoperimetric inequalities;    Projection bodies;    Centroid bodies;    Intersection bodies;    Valuations;   

DOI  :  10.1016/j.jmaa.2020.124190

来源: Elsevier

【 摘 要 】

Lutwak's volume inequalities for polar projection bodies of all orders are generalized to polarizations of Minkowski valuations generated by even, zonal measures on the Euclidean unit sphere. This is based on analogues of mixed projection bodies for such Minkowski valuations and a generalization of the notion of centroid bodies. A new integral representation is used to single out Lutwak's inequalities as the strongest among these families of inequalities, which in turn are related to a conjecture on affine quermassintegrals. In the dual setting, a generalization of volume inequalities for intersection bodies of all orders by Leng and Lu is proved. These results are related to Grinberg's inequalities for dual affine quermassintegrals. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free