The Brunn-Minkowski inequality, Minkowski's first inequality, and their duals'

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:245

Article

Gardner, RJ ; Vassallo, S

关键词: geometric tomography;    star body;    convex body;    Brunn-Minkowski inequality;    Minkowski's first inequality;    mixed volume;    dual Brunn-Minkowski inequality;    dual mixed volume;   

DOI  :  10.1006/jmaa.2000.6774

来源: Elsevier

【 摘 要 】

Quantitative versions are given of the equivalence of the Brunn-Minkowski inequality and Minkowski's first inequality from the Brunn-Minkowski theory. Similar quantitative versions are obtained of the equivalence of the corresponding inequalities from Lutwak's dual Brunn-Minkowski theory. The main results are shown to be the best possible up to constant factors. (C) 2000 Academic Press.

【 授权许可】

Free