Constructs counterexamples showing the symmetric Dyn-Farkhi conjecture fails for n≥3 and proves that the n-fold Minkowski average is the sharp threshold for a guaranteed drop in Hausdorff distance to the convex hull.
Sharp quantitative stability for the Pr\'ekopa-Leindler and Borell-Brascamp-Lieb inequalities
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Characterizes equality cases in Liakopoulos's generalized dual Loomis-Whitney volume estimate using equality cases from Barthe's reverse Brascamp-Lieb inequality.
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The sharp threshold for Hausdorff convexification under Minkowski addition
Constructs counterexamples showing the symmetric Dyn-Farkhi conjecture fails for n≥3 and proves that the n-fold Minkowski average is the sharp threshold for a guaranteed drop in Hausdorff distance to the convex hull.
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Equality in Liakopoulos's generalized dual Loomis-Whitney inequality via Barthe's Reverse Brascamp-Lieb inequality
Characterizes equality cases in Liakopoulos's generalized dual Loomis-Whitney volume estimate using equality cases from Barthe's reverse Brascamp-Lieb inequality.