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Journal of Convex Analysis 24 (2017), No. 3, 807--817
Copyright Heldermann Verlag 2017

Borell's Generalized Prékopa-Leindler Inequality: A Simple Proof

Arnaud Marsiglietti
Institute for Mathematics and its Applications, University of Minnesota, 207 Church Street SE, 434 Lind Hall, Minneapolis, MN 55455, U.S.A.

We present a simple proof of Christer Borell's general inequality in the Brunn-Minkowski theory. We then discuss applications of Borell's inequality to the log-Brunn-Minkowski inequality of K. J. Böröczky, E. Lutwak, D. Yang and G. Zhang [The log-Brunn-Minkowski inequality, Adv. Math. 231 (2012) 1974-1997].

Keywords: Brunn-Minkowski, convex body, log-Brunn-Minkowski inequality, mass transportation.

MSC: 28A75, 52A40

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