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Sharp Quantitative Stability for the Prékopa-Leindler and Borell-Brascamp-Lieb Inequalities
Alessio Figalli, Peter van Hintum, Marius Tiba
The Borell-Brascamp-Lieb inequality is a classical extension of the Prékopa-Leindler inequality, which in turn is a functional counterpart of the Brunn-Minkowski inequality. The st…
Random Translates in Minkowski Sums
Paul Balister, Bela Bollobas, Imre Leader +1
Suppose that and are sets in , and we form the sumset of with random points of . Given the volumes of and , how should we choose them to min…
Sharp L1 Inequalities for Sup-Convolution
Peter van Hintum, Hunter Spink, Marius Tiba
Given a compact convex domain and bounded measurable functions , define the sup-convolution t…
Sharp quantitative stability of the planar Brunn-Minkowski inequality
Peter van Hintum, Hunter Spink, Marius Tiba
We prove a sharp stability result for the Brunn-Minkowski inequality for . Assuming that the Brunn-Minkowski deficit $δ=|A+B|^{\frac{1}{2}}/(|A|^\frac12+|B|…