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

Authors
Gardner, RJ Vassallo, S
Citation
Rj. Gardner et S. Vassallo, The Brunn-Minkowski inequality, Minkowski's first inequality, and their duals', J MATH ANAL, 245(2), 2000, pp. 502-512
Citations number
18
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
ISSN journal
0022247X → ACNP
Volume
245
Issue
2
Year of publication
2000
Pages
502 - 512
Database
ISI
SICI code
0022-247X(20000515)245:2<502:TBIMFI>2.0.ZU;2-A
Abstract
Quantitative versions are given of the equivalence of the Brunn-Minkowski i nequality and Minkowski's first inequality from the Brunn-Minkowski theory. Similar quantitative versions are obtained of the equivalence of the corre sponding inequalities from Lutwak's dual Brunn-Minkowski theory. The main r esults are shown to be the best possible up to constant factors. (C) 2000 A cademic Press.