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.
Vassallo, S. F., Gardner, R. J., The Brunn-Minkowski inequality, Minkowski's first inequality and their duals, <<JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS>>, 2000; (245): 502-512. [doi:10.1006/jmaa.2000.6774] [http://hdl.handle.net/10807/29401]
The Brunn-Minkowski inequality, Minkowski's first inequality and their duals
Vassallo, Salvatore Flavio;
2000
Abstract
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.
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