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The log-Brunn-Minkowski inequality and its local version Putterman, Eli


The conjectured log-Brunn-Minkowski inequality has attracted much interest since its introduction by Böröczky, Lutwak, Yang and Zhang in 2012. In this talk, I shall survey the connections between this inequality and various outstanding problems in convex geometry. Then, I shall discuss the recently discovered local version of the log-Brunn-Minkowski inequality and present a result of the author demonstrating the equivalence of this inequality to the original, 'global' log-Brunn-Minkowski inequality.

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