The Brunn–Minkowski Inequality, Minkowski's First Inequality, and Their Duals

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....

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 245; no. 2; pp. 502 - 512
Main Authors Gardner, R.J., Vassallo, S.
Format Journal Article
LanguageEnglish
Published San Diego, CA Elsevier Inc 15.05.2000
Elsevier
Subjects
Brunn–Minkowski inequality
convex body
dual Brunn–Minkowski inequality
dual mixed volume
Exact sciences and technology
geometric tomography
Mathematical analysis
Mathematics
Minkowski's first inequality
mixed volume
Real functions
Sciences and techniques of general use
star body
dual Brunn–Minkowski inequality
mixed volume
geometric tomography
Minkowski's first inequality
star body
convex body
dual mixed volume
Brunn–Minkowski inequality
Measurable function
Dual inequality
Minkowski metric
Geometric tomography
Tomography
Convex body
Brunn Minskowski inequality
Star body
Inequality
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Summary: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.
ISSN:0022-247X
1096-0813
DOI:10.1006/jmaa.2000.6774