Remark on Stability of Brunn–Minkowski and Isoperimetric Inequalities for Convex Bodies
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This paper is a note on the work of Figalli, Maggi and Pratelli, regarding the stability of Brunn–Minkowski and the isoperimetric inequalities. By a careful examination of the methods presented in the mentioned papers, we slightly improve the constants that appear in stability versions of these inequalities, which play an important role in asymptotic geometric analysis. In addition we discuss a stability version of Urysohn’s inequality and the relation to Dar’s conjecture.
KeywordsConvex Body Isoperimetric Inequality Mixed Volume Minkowski Inequality Mass Transportation
I would like to thank my advisor, professor Vitali Milman, and Professors Figalli and Pratelli for discussions and their useful advices regarding the Brunn Minkowski stability problem. This research was supported by ISF grant 387/09 and BSF grant 200 6079.
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