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On the dimensional Brunn-Minkowski conjecture: the role of symmetry

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No logo availableBanff International Research Station (BIRS) for Mathematical Innovation and Discovery
 Livshyts, Galyna V.

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On the dimensional Brunn-Minkowski conjecture: the role of symmetry
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On the dimensional Brunn-Minkowski inequality
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20
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In the recent years, a number of conjectures has appeared, concerning the improvement of the inequalities of Brunn-Minkowski type under the additional assumptions of symmetry; this includes the B-conjecture, the Gardner-Zvavitch conjecture of 2008, the Log-Brunn-Minkowski conjecture of 2012, and some variants.