Abstract

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].

Author information

Contact details are reproduced from the original publication and may be historical.

Arnaud Marsiglietti

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

arnaud.marsiglietti@ima.umn.edu

Keywords

  • Brunn-Minkowski
  • convex body
  • log-Brunn-Minkowski inequality
  • mass transportation

Mathematics Subject Classification

28A75, 52A40

Suggested citation

A. Marsiglietti. “Borell's Generalized Prékopa-Leindler Inequality: A Simple Proof.” Journal of Convex Analysis 24 (2017), No. 3, 807–817.

Copyright Banach Press 2017