The log-Brunn-Minkowski inequality

Böröczky, Károly (Ifj.) and Lutwak, E. and Yang, D. and Zhang, G. (2012) The log-Brunn-Minkowski inequality. ADVANCES IN MATHEMATICS, 231 (3-4). pp. 1974-1997. ISSN 0001-8708

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Abstract

For origin-symmetric convex bodies (i.e., the unit balls of finite dimensional Banach spaces) it is conjectured that there exist a family of inequalities each of which is stronger than the classical Brunn-Minkowski inequality and a family of inequalities each of which is stronger than the classical Minkowski mixed-volume inequality. It is shown that these two families of inequalities are "equivalent" in that once either of these inequalities is established, the other must follow as a consequence. All of the conjectured inequalities are established for plane convex bodies. © 2012 Elsevier Ltd.

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