Abstract: Starting from a mass transportation proof of the Brunn-Minkowski inequality on convex sets, we improve the inequality showing a sharp estimate about the stability property of optimal sets. This is based on a Poincaré-type trace inequality on convex sets that is also proved in sharp form.
A refined Brunn-Minkowski inequality for convex sets / A. Figalli; F. Maggi; A. Pratelli. - In: ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE. - ISSN 0294-1449. - STAMPA. - 26:(2009), pp. 2511-2519. [10.1016/j.anihpc.2009.07.004]
A refined Brunn-Minkowski inequality for convex sets
MAGGI, FRANCESCO;
2009
Abstract
Abstract: Starting from a mass transportation proof of the Brunn-Minkowski inequality on convex sets, we improve the inequality showing a sharp estimate about the stability property of optimal sets. This is based on a Poincaré-type trace inequality on convex sets that is also proved in sharp form.
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